University  of  California  •  Berkeley 


THE  THEODORE  P.  HILL  COLLECTION 

of 

EARLY  AMERICAN  MATHEMATICS  BOOKS 


. 


' 


BRYANT  AND  STEATTON'S 


•    COMMERCIAL  ARITHMETIC. 


IN     TW  OPART  S. 


DESIGNED 


FOR   THE    COUNTING    ROOM,    COMMERCIAL  AND    AGRICULTURAL 

COLLEGES,    NORMAL    AND    HIGH    SCHOOLS, 

ACADEMIES,   AND  UNIVERSITIES. 


BY 

E.  E.  WHITE,  A.M.,  J.  B.  MERIAM,  A.M., 

SUIT.   PUB.   SCHOOLS,   POBTSMOTJTU,   OHIO.  CASHIER  CITY  BANK,   CLEVELAND,   OHIO. 

AND 

H.   B.  BRYANT,  \AND  H.  D.   STRATTOX, 

FOUNDERS   AND    PROPRIETORS    OF   THE   "NATIONAL   CHAIN    OF   MERCANTILE  COLLEGES," 

LOCATED   AT    NEW    YORK,  PHILADELPHIA,   ALBANY,   BUFFALO,   CLEVELAND, 

DETROIT,    CHICAGO,    AND   ST.    LOUIS. 


NEW   YOEK: 
OAKLEY    AND    MASON. 

1866. 


Entered,  according  to  Act  of  Congress,  in  the  year  1860,  by 

>T.  Jb.  BRYANT  &  H.  D.  STRATTON, 
In  the  Clerk's  Office  of  the  District  Court  tor  tne  Southern  District  of  New  York. 


ELECTBOTTPED  BY 


SMITH    &    McDOUGAL,  J.    M.    JOHNSON, 

82  &  84  Beekman  St.  printer  and  Binder, 

BUFFALO,  N.  Y. 


PREFACE. 


EVERY  book — and  especially  every  text-book — should  have 
a  twofold  reason  for  its  existence :  first,  a  want  which  it  is 
desigi  d  to  meet,  and,  secondly,  an  adaptedness  to  supply  that 
want.  A  work  which  meets  these  conditions  needs  no  apology 
for  its  appearance. 

The  preparation  of  the  present  treatise  was  undertaken  at 
the  earnest  solicitation  of  Messrs.  BRYANT  and  STRATTON. 
Their  intimate  acquaintance  with  the  wants  of  business  students, 
resulting  from  an  extensive  experience  in  Commercial  Instruc- 
tion, revealed  to  them  an  urgent  demand  for  such  a  work,  and 
suggested  its  general  plan. 

The  Authors  have  also  been  engaged,  many  years,  as  teachers 
of  Arithmetic  and  Commercial  Calculations  in  the  first  schools 
and  commercial  colleges  of  the  country,  or  in  some  of  the  most 
practical  departments  of  business.  The  result  of  this  experience 
is  the  conviction  that  a  work  presenting  fully  the  applications  of 
arithmetic  to  actual  business,  and  discussing  thoroughly  the  gen- 
eral principles  of  mercantile  transactions,  has  long  been  a  desid- 
eratum. True,  there  are  some  excellent  works  on  arithmetic, 
in  which  considerable  space  is  devoted  to  business  forms  and 
transactions.  In  no  one  of  these,  however,  with  which  we  are 
acquainted,  are  these  subjects  treated  with  sufficient  fullness  or 
thoroughness  for  commercial  students.  By  searching  through 
half  a  score  of  the  best  arithmetics  now  published,  most  of  the 
mformation  designed  may  possibly  be  obtained.  The  present 
treatise  embodies  this  information  in  one  volume,  and  presents, 
in  part,  our  idea  of  what  is  needed. 


IV  PREFACE. 

PART  FIRST  is  designed  to  afford  a  review  of  elementary 
arithmetic.  In  its  preparation  it  has  been  assumed  that  the 
student  possesses  some  knowledge  of  numbers.  Fractions, 
common  and  decimal,  and  Ratio  and  Proportion  are  treated 
with  considerable  thoroughness  on  account  of  their  great  im- 
portance. 

PART  SECOND  is  devoted  mainly  to  Commercial  Calcu- 
lations. Aside  from  clear  and  exact  definitions,  concise  rules, 
and  lucid  explanations,  we  have  endeavored  to  present  a  system 
of  general  principles  relating  to  the  different  subjects  which 
will  enable  the  student  more  fully  to  understand  the  nature  and 
true  theory  of  business  transactions.  To  secure  accuracy,  por- 
tions of  the  manuscript  have  been  submitted  to  the  supervision 
of  business  men  familiar  with  the  subjects  treated  of. 

As  the  value  of  such  a  work  as  this  greatly  depends  upon  the 
character  of  its  problems,  we  have  aimed  to  present,  as  far  as 
possible,  those  occurring  in  actual  business,  without  specially 
preparing  them  for  the  place  they  occupy. 

Experience  and  observation  have  taught  us,  in  relation  to 
money,  banks,  interest,  and  exchange,  that  business  students 
need  something  more  than  rules,  forms,  and  tables.  They  want 
the  theory  too.  The  various  and  contradictory  opinions  upon 
these  subjects  set  forth  by  business  men  of  even  considerable 
experience,  prove  a  lack  of  knowledge  of  first  principles  which 
should  incite  the  student  to  a  very  thorough  examination  for 
himself.  Money  has  intrinsic  properties,  and  is  controlled  by 
natural  laws,  some  of  the  most  important  of  which  we  have 
endeavored  to  present. 

The  nature  of  Interest,  and  the  principles  of  Exchange  and 
Balance  of  Trade  are  also  fully  explained,  and,  if  found  correct, 
will  necessarily  expose  some  radical  but  popular  errors.  The 
problems  submitted  will  be  found  to  contain  satisfactory  facts 
and  statistics  supporting  our  views. 


PREFACE.  V 

The  difference  between  simple,  annual,  and  compound  inter- 
est, and  the  operation  of  the  different  rules  for  finding  the 
amount  due  on  notes  when  "partial  payments"  have  been 
made,  are  illustrated  by  diagrams.  The  treatment  of  annual 
interest  is  the  joint  work  of  the  authors,  and  is  believed  to  be 
worthy  of  special  attention. 

In  the  Equation  of  Payments  and  the  Equation  of  Accounts 
we  have  aimed  to  make  the  student  a  rule  to  himself.  The 
rules  and  processes  recommended  are  the  results  of  a  clear 
analysis,  leading  the  student  with  "open  eyes"  into  the  usual 
perplexities  of  these  subjects. 

The  first  116  pages  of  the  work,  also  the  articles  on  Equation 
of  Payments,  Equation  of  Accounts,  Cash  Balance,  Annuities, 
Partnership,  Alligation,  Duodecimals,  Involution  and  Evolution, 
were  prepared  by  Mr.  E.  E.  WHITE  ;  the  articles  on  Interest, 
Partial  Payments,  Currency  and  Money,  Banks  and  Banking, 
Exchange,  Prommissory  Notes,  Stocks  and  Bonds,  Progression 
and  Mensuration,  by  Mr.  J.  B.  MERIAM.  Partnership  Settle- 
ments aod  a  portion  of  the  Supplement  were  written  by  Messrs. 
BRYANT  and  STRATTOX,  to  whom  we  also  acknowledge  our 
indebtedness  for  valuable  materials  and  suggestions. 

The  work  has  been  extended  beyond  its  first  design,  to  adapt 
it  to  advanced  classes  in  our  High  Schools  and  Academies,  and 
is  now  believed  to  be  sufficiently  elementary  and  extensive  for 
that  purpose. 

E.  E.  WHITE. 
J.  B.  MERIAM. 

December,  1860. 


IN  committing  this  work  to  the  hands  of  the  gentlemen  who 
are  known  as  its  authors,  we  have  been  actuated  by  the  sole 
purpose  of  producing  a  book  which  should  possess  all  the  requi- 
sites of  a  first-class  business  Arithmetic  in  a  greater  degree  than 
any  previous  work.  We  are  aware  that  many  books  are  already 
extant  which  may  well  dispute  the  ground  as  elaborately  scien- 
tific essays  upon  the  properties  of  numbers,  but  we  are  as  fully 
conscious  that  few,  if  any,  can  be  found  which  will  so  completely 
answer  the  demands  of  the  student  of  Accounts  or  the  practical 
business  man,  as  the  present  treatise. 

The  principal  authors  of  this  work  are  men  of  large  expe- 
rience and  ripe  judgment,  both  in  the  general  acceptation  and  in 
their  respective  departments  of  life.  Mr.  WHITE  has  been  for 
many  years  connected  with  public  education  in  such  capacities  as 
would  essentially  prepare  him  to  appreciate  the  wants  of  the 
learner,  while  his  associate,  Mr.  MERIAM,  has  had  equal  advan- 
tages in  the  more  practical  details  of  business,  as  well  as  ample 
experience  in  teaching.  We  think  it  would  be  difficult,  if  not 
impossible,  to  combine  better  qualifications  for  this  particular 
work. 

To  be  brief,  the  book  suits  us ;  and  while  we  shall  heartily 
adopt  it  in  our  extensive  chain  of  business  schools,  we  shall 
have  no  delicacy  in  pressing  its ,  claims  upon  educators  and 
business  men  throughout  the  country,  feeling,  as  we  do,  that  in 
promoting  its  general  circulation,  we  are  doing  much  for  the 
cause  which  is  dearer  to  us  than  all  others;  that  of  PRACTICAL 
EDUCATION. 

H.  B.  BRYANT. 
H.  D.  STRATTON. 


TABLE    OF    CONTENTS. 


PART    FIRST. 

PAGE 

NUMERATION  AND  NOTATION, 13 

ANALYSIS  OF  NUMBERS, 15 

ADDITION, 17 

LEDGER  COLUMNS, 18 

THE  ADDING  OP  SEVERAL  COLUMNS, 20 

SURTRACTION, 21 

MULTIPLICATION, 22 

DIVISION, 23 

CONTRACTIONS  IN  MULTIPLICATION  AND  DIVISION, 23 

When  the  Multiplier  is  14,  15,  16,  etc., 24 

When  the  Multiplier  is  31,  41,  51,  etc., 24 

To  Multiply  by  any  two  figures, 25 

To  Multiply  by  a  convenient  part  of  10, 100,  1000,  etc., 25 

To  Divide  by  a  convenient  part  of  10,  100,  1000,  etc., 26 

FEDERAL  MONEY, 27 

BILLS, 28 

GREATEST  COMMON  DIVISOR, 32 

LEAST  COMMON  MULTIPLE, 34 

COMMON  FRACTIONS, 36 

To  Reduce  a  Fraction  to  its  Lowest  Terms, 37 

To  Reduce  a  Fraction  to  its  Higher  Terms, 38 

To  Reduca  an  Improper  Fraction  to  a  "Whole  or  Mixed  Number, 39 

To  Reduce  a  Whole  or  Mixed  Number  to  an  Improper  Fraction, 39 

To  Reduce  Compound  Fractions  to  Simple  Ones, 40 

CANCELLATION, 41 

To  Reduce  Fractions  to  a  Common  Denomination, 42 

ADDITION  OF  COMMON  FRACTIONS, 43 

SUBTRACTION  OF  COMMON  FRACTIONS, 44 

MULTIPLICATION  OF  COMMON  FRACTIONS. 45 

To  Multiply  a  Fraction  by  a  Whole  Number, 45 

To  Multiply  a  Whole  Number  by  a  Fraction, 45 

To  Multiply  one  Fraction  by  another, 46 


Viii  CONTENTS. 

PAtfB 

DIVISION  OF  COMMON  FRACTIONS, 47 

To  Divide  a  Fraction  by  a  Whole  Number, 47 

To  Divide  a  Whole  Number  by  a  Fraction, 47 

To  Divide  one  Fraction  by  another, 48 

To  Keduce  a  Complex  Fraction  to  a  Simple  One, 49 

MISCELLANEOUS  PROBLEMS  IN  COMMON  FRACTIONS, , 50 

DECIMAL  FRACTIONS, ; 52 

NUMERATION  OP  DECIMALS, 54 

NOTATION  OF  DECIMALS, 55 

REDUCTION  OF  DECIMALS, 56 

To  Reduce  a  Decimal  to  a  Common  Fraction, 56 

To  Reduce  a  Common  Fraction  to  a  Decimal, 57 

ADDITION  OF  DECIMALS, 58 

SUBTRACTION  OF  DECIMALS, 59 

MULTIPLICATION  OF  DECIMALS, 60 

.DIVISION  OF  DECIMALS, 60 

To  Divide  a  Decimal  by  10,  100,  1000,  etc., 62 

To  Multiply  a  Decimal  by  10,  100,  1000,  .1,  .01,  .001,  etc., 62 

REDUCTION  OF  DENOMINATE  NUMBERS, 63 

To  Reduce  a  Denominate  Number  of  a  Higher  Denomination  to  a  Lower,  63 

To  Reduce  a  Denominate  Number  of  a  Lower  Denomination  to  a  Higher,  65 

To  Find  what  part  one  Denominate  Number  is  of  another, 66 

To  Reduce  a  Fraction  of  a  Higher  Denomination  to  Integers  of  a  Lower,  67 

ADDITION  OF  DENOMINATE  NUMBERS, 68 

SUBTRACTION  OF  DENOMINATE  NUMBERS, 69 

MULTIPLICATION  OF  DENOMINATE  NUMBERS, 70 

DIVISION  OF  DENOMINATE  NUMBERS, 70 

MISCELLANEOUS  PROBLEMS, 71 

PRACTICE, 73 

RATIOS, 77 

SIMPLE  PROPORTION, 78 

COMPOUND  PROPORTION, 81 


PART    SECOND. 

PERCENTAGE, 84 

To  Express  the  Rate  Per  Cent.  Decimally, 84 

To  Find  a  Given  Per  Cent  of  any  Number, . . '. 85 

To  Find  what  Per  Cent,  one  Number  is  of  another, 87 

To  Find  a  Number  when  a  certain  Per  Cent,  is  given, 88 

A  Number  being  given,  a  certain  Per  Cent,  more  or  less  than  another,  to 

find  the  latter, 89 

APPLICATION  OF  PERCENTAGE, 90 


CONTENTS.  IX 

PAGB 

PROFIT  AND  Loss 91 

COMMISSION  AND  BROKERAGE 96 

INSURANCE — Fire  and  Marine , 98 

LIFE  INSURANCE 102 

TAXES 103 

TAX  TABLES 105 

DUTIES  OR  CUSTOMS 106 

Specific  Duties 107 

BANKRUPTCY 109 

STORAGE 110 

GENERAL  AVERAGE.  . .  t 114 

INTEREST 117 

Simple  Interest 119 

Computation  of  Time  in  Interest 123 

PRESENT  WORTH  AND  DISCOUNT c 127 

ANNUAL  INTEREST 128 

COMPOUND  INTEREST 131 

PARTIAL  PAYMENTS — Three  Rules 138 

Vermont  Rule 138 

United  States  Rule 139 

Mercantile  Rule 142 

Merits  of  the  Three  Rules 143 

Diagram  Illustrating  Simple,  Annual,  and  Compound  Interest 145 

Diagrams  Illustrating  Partial  Payments , 149-151 

METALLIC  CURRENCY «...  152 

PAPER  CURRENCY 155 

BANKS  OF  DEPOSIT 159 

BANKS  OF  DISCOUNT 1G1 

BANKS  OF  ISSUE 161 

BANKS  OF  EXCHANGE 163 

EXCHANGE   163 

PAR  OF  EXCHANGE „...._ 165 

RULE  FOR  COMPUTING  STERLING  EXCHANGE 166 

NOMINAL  EXCHANGE  OR  AGIO 167 

COURSE  OF  EXCHANGE 169 

BALANCE  OF  TRADE  AND  BALANCE  OF  PAYMENTS 170 

STATISTICS 173 

EXAMPLES  IN  EXCHANGE 175 

BILLS  OF  EXCHANGE 180 

PROMISSORY  NOTES 181 

NEGOTIABLE  PAPER 182 

^  Liability  of  Parties  connected  \vith  Negotiable  Paper 183 

PRESENTMENT,  PROTEST,  AND  NOTICE c . .  185 

DAYS  OF  GRACE  AND  TIME  OF  MATURITY 186 

DISCOUNTING  NOTES 188 

* 


X  CONTENTS. 

PAGE 

BANK  DISCOUNT 190 

BANKERS'  ACCOUNT  CURRENT 192 

ROLES  FOR  DETECTING  ERRORS  IN  TRIAL  BALANCES. 194 

STOCKS  AND  BONDS 197 

Railroad  Stocks 198 

State  Stocks 198 

Government  Stocks 198 

Consuls 198 

NEW  RULE  FOR  FINDING  THE  VALUE  OF  A  BOND 201 

EQUATION  OF  PAYMENTS 204 

To  find  the  Equated  Time  for  the  Payment  of  several  Sums  of  Money 

with  Different  Terms  of  Credit 204 

Method  by  Products 205 

Method  by  Interest 205 

Proof  of  Correctness  of  Mercantile  Method 206 

"  Accurate  Rule"  not  accurate „ ,  207 

To  find  Equated  Time  for  Payment  of  several  Sales  made  at  Different 

Dates  and  at  Different  Terms  of  Credit 211 

To  find  what  Extension  should  be  given  to  the  Balance  of  a  Debt,  Par- 
tial Payments  having  been  made  before  the  Debt  was  Due 215 

EQUATION  OF  ACCOUNTS 217 

Two  Methods 218 

Another  Method 221 

CASH  BALANCE „ 224 

Account  of  Sales 227 

ANNUITIES 230 

Annuity  Tables 231 

To  find  the  Final  Value  of  an  Annuity  Certain 232 

To  find  the  Present  Value  of  an  Annuity  Certain 232 

To  find  the  Present  Value  of  a  Perpetuity 233 

To  find  the  Present  Value  of  an  Annuity  Certain  in  Reversion 233 

To  find  the  Annuity,  the  Present  or  Final  Value,  Time,  and  Rate  being 

given 234 

Contingent  Annuities, 235 

To  find  the  Present  Value  of  a  Lifo  Annuity 236 

ALLIGATION .' 237 

Alligation  Medial 237 

Alligation  Alternate „ 239 

Method  by  Linking" 240 

PARTNERSHIP 243 

Capital  Invested  same  Length  of  Time. 244 

Capital  Invested  for  Different  Periods  of  Time. . . 246 

DUODECIMALS -f»  249 

Multiplication  of  Duodecimals W. »  249 

INVOLUTION..  .., 251 


CONTENTS.  Xi 

PAGE 

EVOLUTION 253 

SQUARE  ROOT 254 

The  Eight-Angled  Triangle 258 

CUBE  ROOT .* 260 

ARITHMETICAL  PROGRESSION 264 

GEOMETRICAL  PROGRESSION 267 

MENSURATION 270 

Triangles 272 

To  Find  the  Area  of  a  Triangle 272 

Quadilaterals,  Pentagons,  &c 273 

To  find  the  Area  of  any  Quadrilateral  having  Two  Sides  Parallel.. .  273 

To  find  the  Area  of  a  Regular  Polygon 273 

To  find  the  Area  of  an  Irregular  Polygon  of  Two  Sides  or  more 273 

Circles 274 

To  find  the  Circumference  of  a  Circle,  the  Diameter  being  known. .  275 

To  find  the  Diameter  of  a  Circle,  the  Circumference  being  known. .  275 

To  find  the  Area  of  a  Circle,  the  Diameter  being  known 275 

To  find  the  Area  of  a  Circle,  the  Circumference  being  known 275 

To  find  the  Area  of  a  Circle,  the  Circumference  and  Diameter  both 

being  known 275 

To  find  the  Diameter  or  Circumference  of  a  Circb,  the  Area  being 

known 275 

To  find  the  Side  of  the  largest  Square  that  can  be  inscribed  in  a 

Circle 275 

To  find  the  side  of  the  largest  Equilateral  Triangle  that  can  be  in- 
scribed in  a  Circle 275 

Ellipse 276 

To  find  the  Area  of  an  Ellipse,  the  two  Diameters  being  given 276 

MENSURATION  OP  SOLIDS 276 

Prisms  and  Cylinders 276 

To  find  the  entire  Surface  of  a  Right  Prism  or  Right  Cylinder 277 

To  find  the  Solidity  of  a  Prism  or  Cylinder 277 

Pyramids  and  Cones 277 

To  find  the  entire  Surface  of  a  Regular  Pyramid,  or  of  a  Cone 278 

To  find  the  Solidity  of  any  Pyramid  or  Cone 278 

To  find  the  entire  Surface  of  a  Frustrum  of  a  Right  Pyramid  or  of  a 

Cone 278 

Spheres 278 

To  find  the  Surface  of  a  Sphere 279 

To  find  the  Solidity  of  a  Sphere 279 

Gauging 279 

PARTNERSHIP  SETTLEMENTS 280 

The  Investment,  the  Resources,  and  Liabilities  being  given,  to  find  the 

nr "-  Gam  cr  Loss. . .                                                                       281 


Xll  CONTENTS. 

PAGE 

The  Investment,  the  Resources,  and  Liabilities  at  Closing,  and  the  Pro- 
portion in  which  the  Partners  share  the  Gains  or  Losses  being  given, 
to  find  each  Partner's  Interest  in  the  Concern  at  Closing 282 

The  Resources,  the  Liabilities  (excefrt  the  Investment),  and  the  net  Gain 

or  Loss  being  given,  to  find  the  net  Capital  at  commencing 285 

("When  the  Firm  commence  Insolvent.)  The  Resources  and  Liabilities  at 
Closing,  and  the  net  Gain  or  Loss  being  given,  to  find  the  net  In- 
solvency at  commencing 287 

Miscellaneous  Examples 290 


SUPPLEMENT 299 

Rates  of  Interest  and  Statute  Limitations  in  the  United  States 299 

Exchange  Tables 300 

Foreign  Coins— Gold 304 

«  «    —Silver 305 

Tables  of  Weights  and  Measures. , 306 

Practical  Hints  to  Farmers 312 

Table  of  Money,  "Weight,  and  Measure  of  the  Principal  Commercial  Coun- 
tries in  the  "World 312 

Miscellaneous  Table  of  Foreign  "Weights  and  Measures 322 

Rates  of  Foreign  Money  or  Currency,  fixed  by  Law 323 

A  Table  of  Foreign  Weights  and  Measures,  reduced  to  the  Standard  of 
the  United  States,  and  as  received  at  the  United  States  Custom 

Houses • 324 

Table  giving  th%  Currency,  Rate  of  Interest,  Penalty  for  Usury,  and  Laws 
in  regard  to  the  Collection  of  Debts,  &c.,  in  the  several  United 
States..  326 


PART     FIRST, 

NUMERATION    AND    NOTATION, 


ART.  1.  Numbers  are  composed  of  orders,  the  value  of 
whose  unit  increases  from  right  to  left  in  a  ten-fold  ratio,  that 
is,  ten  units  of  any  order  make  one  unit  of  the  order  next 
higher.  The  names  of  the  first  twelve  orders  are  as  follows  : 


indieds  of  liil 

\ 
2 

<D 

a 
•5 

indivds  of  Mi 

CO 

g 

i 

1 

indreds  of  Tli 

ns  of  Thoimi 

ousands. 
ndrods. 

- 

I 

- 

— 

i 

p^ 

H 

rfl                    » 

H       B 

1   1 

E 

8 

5 

8 

8 

5 

5 

8 

8      8 

8      3 

£ 

4:        Ji 

1 

0 

a 

o 

o 

0 

0 

0 

o     o 

0       0 

000000000000 
For  convenience  in  reading  or  writing  numbers,  we  divide 
the  orders  into  periods  of  three  figures  each.  The  three  orders 
which  compose  any  period  are  called  Units,  Tens,  Hundreds 
of  that  period.  The  following  table  presents  the  names  of  the 
periods  and  the  manner  of  reading  them  : 

£  5  a  H  t§ 


£n;5     SH&     ££3     «££     £££ 
333    333    333    333    333 

Wi  Period.  Uh  Period.  3d  Period.  Zd  Period.  1st  Period. 


14  NUMERATION     AND     NOTATION. 

The  names  of  the  periods  above  Trillions  are  Quadrillions, 
Quintillions,  Sextillions,  Septillions,  Octillions,  Nonillions, 
Decillions,  etc. 

ART.  2.  To  read  a  number  composed  of  more  than  three 
figures,  we  have  the  following 

R-  U  JL,  E) . 

Begin  at  the  right  hand  and  divide  the  number  into  periods 
of  three  figures  each.  Then,  commencing  at  the  left  hand,  read 
the  figures  of  each  period  as  if  it  stood  alone,  adding  the  name 
of  the  period. 

Remark. — 1.  The  name  of  the  first  or  unit  period  is  gener- 
ally omitted. 

2.  Beginners  should  first  be  taught  to  read  and  write  num- 
bers composed  of  not  more  than  three  figures.  Perfect  accu- 
racy in  this  is  very  important. 

Examples. 

1.  203. 

2.  230. 

3.  40404. 

4.  3060800. 

5.  402300060. 

6.  3700070707. 

7.  30303030303. 

8.  4000400040004. 

9.  32400423000203. 
10.                             801001089006007. 

Note. — In  separating  a  number  into  periods,  use  a  comma. 
ART.  3.  To  write  a  number  by  figures,  we  have  the  follow- 
ing 

R.TJLE. 

Beginning  at  the  left  hand,  write  the  figures  of  each  period 
as  if  it  were  to  stand  alone,  taking  care  to  fill  up  the  vacant 
orders  or  periods  with  ciphers. 

Note. — We  may  begin  at  the  right  hand  instead  of  the 
left.  The  latter  is  preferable,  however. 


NUMERATION    AND     NOTATION.  15 

E  x  a,  m  pies. 

1.  Express  in  figures  forty  millions,  four  hundred  and  six 
thousand,  and  five. 

Explanation. — First  write  40,  and  place  after  it  a  comma 
to  separate  it  from  the  next  lower  period,  thus  :  40,  ;  next 
write  406  in  thousand's  period,  and  place  a  comma,  thus  : 
40,406, ;  then  write  5  in  unit's  period,  and  fill  up  the  two 
vacant  orders  with  ciphers,  thus  :  40,406,005. 

2.  Express  in  figures  sixty-five  billions,  twenty  thousand, 
and  eighty. 

Explanation. — Write  65,  and  place  after  it  a  comma,  thus  : 
65,  ;  then,  as  the  next  period  (millions)  is  not  given,  fill  it 
with  ciphers,  and  place  after  it  a  comma  ;  thus  :  65,000,  ; 
then  write  20,  with  a  comma  after  it,  in  thousand's  period,  fill- 
ing the  vacant  order  with  a  cipher,  thus  :  65,000,020,  ;  lastly 
write  eighty  in  unit's  period,  filling  the  vacant  order  with  a 
cipher,  thus  :  65,000,020,080. 

3.  Express  in  figures  thirty  thousand  and  thirty. 

4.  Four  hundred  millions,  five  thousand  and  six'ty. 

5.  Forty  billions,  forty  thousand  and  forty. 

6.  Ten  trillions,  two  hundred  millions,  one  hundred  and 
one. 

7.  Thirty-five  millions  and  twenty-five  thousand. 

8.  Two  billions,  three  hundred  and  forty-five  millions. 

9.  Nine  trillions,  ninety-nine  millions,  nine  hundred  and 
ninety-nine. 

10.  Forty  trillions  and  ten. 


ANALYSIS  OF  NUMBEKS. 

ART.  4.  In  addition  and  multiplication  of  numbers  it  is 
necessary  to  reduce  units  of  a  lower  order  to  units  of  a  higher  ; 
in  subtraction  and  division  to  reduce  units  of  a  higher  order  to 
units  of  a  lower.  It  is,  also,  often  necessary  to  change  the 
form  of  a  number,  that  is,  take  from  it  as  many  hundreds,  or 
tens,  etc.,  as  possible,  and  read  the  rest  in  units  ;  or  to  reduce  a 


16  NUMERATION     AND     NOTATION. 

part  of  the  units  of  a  higher  order  to  some  lower,  and  express 
the  true  value  of  the  whole.  A  few  examples  will  make  these 
changes  plain  to  the  pupil. 

1.  How  many  units  in  4  tens  ? 

2.  How  many  units  in  4  hundreds  ? 

3.  How  many  tens  in  6  hundreds  ? 

4.  How  many  tens  in  6  thousands  ? 

5.  How  many  hundreds  in  3  millions  ? 

6.  How  many  hundreds  in  2  ten- thousands  ? 

7.  How  many  tens  in  25  thousands  ?  Ans.  2500. 

8.  How  many  tens  in  40  units  ? 

9.  How  many  tens  in  400  units  ?  Ans.  40. 

10.  How  many  hundreds  in  2000  units  ? 

11.  How  many  hundreds  in  200  tens  ? 

12.  How  many  millions  in  2400000  tens  ?          Ans.  24. 

13.  How  many  thousands  in  400  tens  ? 

14.  What  is  the  greatest  number  of  hundreds  that  can  t)<? 
taken  from  34674  ?  Ans.  346. 

15.  Divide  30460  into  hundreds  and  units. 

Ans.  304  hundreds  and  60  units. 

16.  Divide  23046203  into  ten-thousands  and  units. 

Ans.  2304  ten-thousands  and  6203  units. 

17.  Change  the  form  of  23046. 

Explanation. — By  reducing  the  orders,  a  great  number  of 
forms  may  be  given  to  the  number.  The  following  are  some 
of  the  results  :  1  ten-thousand,  130  hundreds,  and  46  units  ; 
129  hundreds,  14  tens,  and  6  units  ;  22  thousands,  9  hundreds, 
13  tens,  and  16  units  ;  and  2  ten-thousands,  304  tens,  and 
6  units.  By  writing  the  changed  form  above  the  natural,  we 
may  have : 

1129146  2210316  11210316  20-29-13-16 

23046;  or  23046  ;  or  23046  ;  or  2  30  46. 

Note. — The  student  should  study  the  above  changes  closely. 
See  that  they  are  clearly  understood. 


ADDITION.  17 


ADDITION. 

ART.  5.  The  two  most  important  qualities  of  an  accountant 
are  accuracy  and  rapidity.  Every  accountant  must  know  that 
his  results  possess  absolute  accuracy.  In  business,  he  is  some- 
times obliged  to  spend  hours,  and  even  days,  in  detecting  an 
error  of  a  few  cents  in  a  trial  balance  sheet.  Kapidity  in  the 
performance  of  his  work  is  of  almost  equal  importance.  The 
most  rapid  computers  are,  generally,  the  most  accurate. 

It  is  not  good  policy  to  wait  for  the  practice  of  actual 
business  to  impart  this  skill.  The  persevering  student  can 
easily  acquire  a  high  degree  of  proficiency,  and  thus  bring  to 
his  business  one  of  the  surest  elements  of  success. 

Addition  is  not  only  the  basis  of  all  numerical  operations, 
but  is  actually  the  most  frequently  used  in  all  departments  of 
business.  It  is,  also,  in  adding  that  the  young  accountant  pos- 
sesses the  least  skill  and  is  most  liable  to  make  mistakes.  For 
these  reasons,  the  student  should  regard  no  labor  too  great 
which  is  necessary  to  master  it.  To  aid  him  in  acquiring 
facility  and  certainty  in  adding  columns  of  figures,  the  follow- 
ing methods  and  suggestions  are  recommended. 

Let  it  be  required,  for  example,  to  add  the  following  num- 
bers : 

637 

584 

796 

839 

376 

458 

749 

276 

968 

Ans.  5683 

Process. — Beginning  at  the  bottom  of  the  right  hand 
column,  and  naming  only  results,  add  thus  :  14,  23,  31,  37,  46, 
52,  56,  63  ;  then  adding  the  6  tens  to  the  second  column,  add 
it  in  the  same  manner— 12,  19,  23,  28,  35,  etc.  The  student 
should  never  permit  himself  to  spell  his  way  up  a  column  of 

2 


18  ADDITION. 

figures  in  this  manner,  viz.  :  8  and  6  are  14,  14  and  9  are  23, 
23  and  8  are  31,  31  and  6  are  37,  etc.  It  is  just  as  easy  to 
name  only  the  results,  and  much  more  rapid. 

Proof. — To  test  the  accuracy  of  the  result,  add  the  columns 
downward. 

Examples. 

1.  Add  57,  63,  246,  788,  565,  399,  464,  and  555. 

2.  Add  36,  69,  304,  5698,  4536,  40864. 

3.  Add  28,  47,  55,  66,  77,  88,  99,  and  23. 

4.  What  is  the  sum  of  309  +  384+679+436  +  358+804+ 
506  +  988+777? 

5.  What  is  the  sum  of  14+16  +  34+86+37+65+56+ 
78+35+49  +  12  +  15+8+9+76  ? 


LEDG-ER    COLUMNS. 

* 

ART.  6.  In  adding  long  columns  of  figures,  as  in  a  Ledger, 
the  following  method  is  sometimes  used  : 

Add  the  columns  in  order,  and  place  the  footings  under 
each  other  upon  a  separate  piece  of  paper  (testing  the  accuracy 
of  the  same  by  proof)  ;  point  off  the  right  hand  figure  (except 
in  the  last  column)  and  add  the  left  hand  figure  or  figures  to 
the  next  column,  thus  : 
'  $57.45 

28.75  Process. 

36.87  4.7 
4.56                                 4.7 

98.88  6 1~~ 
6.25                                 29 

49.38 
9.63 

$291.77 

The  figures,  expressing  the  sum  of  the  left  hand  column, 
together  with  the  figures  cut  off  on  the  right,  read  upivards7 
will  be  the  sum  total.  The  advantage  of  this  method  is  two- 
fold :  1.  The  partial  results  being  preserved,  it  is  easier  to  de- 
tect errors. — Any  column  may  be  re-added  without  the  trouble 


ADDITION. 


19 


of  adding  the  preceding.  2.  The  total  sum  when  written  is 
correct,  and  the  page  is  not  defaced  by  erasures  and  corrections. 

The  student  should  write  out  long  ledger  columns  on  slips 
of  paper,  and  daily  practice  in  adding  them,  being  as  careful 
to  obtain  a  correct  result  as  he  would  be  in  actual  business. 

The  following  ledger  columns  are  given  merely  as  examples. 
The  student  can  easily  increase  the  number  of  them  to  any 
extent. 


1. 

3.25 

8.37 
2.50 
12.35 
9.00 
.88 
.93 
4.65 
5.48 
10.12 
1.20 
9.15 
7.75 
18.64 
9.15 
13.48 
4.96 
8.30 
4.55 
3.08 
1.13 
2.63 
7.87 
4.33 
0.00 
.85 
.90 
5.00 
8.00 
12.00 
15.00 
6.50 
5.80 
7.26 


2. 

32.56 
8.15 
6.33 
17.09 
.90 
.75 
3.25 
21.87 
22.20 
7.15 
4.32 
78.90 
18.88 
3.33 
1.38 
.63 
.49 
50.63 
24.88 
15.33 
10.00 
16.56 
7.77 
5.00 
4.33 
12.34 
17.15 
20.00 
8.50 
8.76 
5.48 
17.10 
22.05 
7.29 
8.99 


3. 
75.50 

284.38 
3287.15 

111.01 
43.96 

263.55 
1900.09 
1356.63 

15.20 
7.15 

13.48 
3456.38 

348.54 
2.75 

52.30 

900.90 

4658.30 

222.56 

914.53 

64.50 

49.87 

302.58 

1256.29 

10.10 
100.98 

78.60 

44.50 
253.63 

77.88 

1860.12 

973.53 

19.10 

28.25 

39.10 
135.00 


4. 

19.50 
23.86 
12.45 
14.52 
25.48 
42.54 
8.60 
9.37 
8.80 
.65 
.73 
.38 
11.25 
.86 
2.95 
5.92 
9.52 
.88 
.99 
6.01 
7.83 
1.50 
2.00 
3.85 
5.38 
1.53 
12.60 
19.30 
22.33 
10.19 
9.81 
8.76 
12.57 
18.19 
7.63 


20  ADDITION. 


THE  ADDING-  OF  SEVERAL  COLUMNS. 

ART.  7.  Considerable  practice  will  enable  the  accountant  to 
add  two  or  more  columns  at  one  operation.  There  is  often  an 
advantage  in  adding  in  this  manner.  Beyond  two  columns,  or 
at  most  three,  the  method  may  be  more  skillful  than  practical. 
The  following  will  illustrate  the  method  of  adding  two  columns : 

86 
75 

68 

34 

__59 

Ans.  322 

Process.— 59  plus  30=89,  plus  4=93,  plus  60=153,  plus 

8=161,  plus  70=231,  plus  5=236,  plus  80=316,  plus  6=322. 

It  will  be  seen  that  the  process  consists  simply  in  adding 

the  tens  first  and  then  the  units.     By  naming  only  the  results, 

we  have  89,  93  ;  153,  161 ;  231,  236  ;  316,  322. 

The  units  may  be  added  first  and  then  the  tens,  thus  :  63, 
93  ;  101,  161 ;  166,  236  ;  242,  322. 

Three  or  more  columns  may  be  added  in  a  similar  manner, 

thus : 

223 
425 
384 
256 

Ans.  1288 

Operation.— 256+4=260,  260+80=340,  340+300=640, 
640  +  5  =  645,  645+20  =  665,  665  +  400  =  1065,  1065  +  3= 
1068,  1068+20=1088,  1088+200=1288. 

By  naming  only  results,  we  have  :  260,  340,  640  ;  645,  665, 
1065  ;  1068,  1088,  1288. 


Examples. 

1.  Add  25,  68,  67,  83,  37,  46,  99,  87,  and  34. 

2.  Add  38,  46,  92,  37,  83,  46,  52,  53,  and  46. 

3.  Add  286,  356,  396,  423,  345,  660,  and  780. 

4.  Add  384,  236,  112,  345,  784,  569,  and  963. 


SUBTRACTION.  21 


SUBTRACTION. 
AET.  8.  Ex.  1.  From  3084  take  2793. 

2  9  IS  4  Minuend  changed  in  form. 

3084  Minuend. 
2793  Subtrahend. 
291  Kemainder. 

Remarks. — 1.  That  the  changed  minuend  above  is  equiva- 
lent to  the  given  minuend  is  evident  from  the  fact  that  30 
hundreds +  8  tens=29  hundreds +  18  tens. 

2.  Upon  the  principle  that  the  difference  between  two 
numbers  is  the  same  as  the  difference  between  these  numbers 
equally  increased,  instead  of  changing  the  form  of  the  minu- 
end, we  can  add  10  to  the  minuend  figure  when  it  is  less  than 
the  lower  subtrahend  figure,  and  add  1  to  the  next  higher  order 
of  the  subtrahend.  It  is  plain  that  1  added  to  a  higher  order 
is  the  same  as  10  added  to  the  next  lower.  We  do  not  borrow 
this  10  however,  nor  do  we  pay  any  thing  by  adding  the  1. 
These  terms  ought  not  to  be  used. 

Examples. 

2.  From  406309  take  347278. 

3.  From  100102  take  90903. 

4.  From  5000050  take  86432. 

5.  From  one  billion  take  one  million  and  one. 

6.  From  32670804  take  3867498. 

7.  From  30006070  take  4906007. 

8.  From  40  hundreds  take  25  tens.  Ans.  3750. 

9.  From  205  tens  take  264  units. 

10.  From  230  tens  take  12  hundreds.  Ans.  1100. 

11.  From  2  millions  take  2  thousands. 

12.  From  16  tens  take  75  units. 

13.  From  101  thousand  take  56  hundreds. 

14.  From  1  ten  take  8  units. 


22  MULTIPLICATION. 


MULTIPLICATION. 

ART.  9.  Ex.  1.  Multiply  3464  by  306. 

Multiplicand,         3464 
Multiplier,      306 

20784 
10392 

Product,  1059984 

Proof  ~by  excess  of  9's. — Add  the  figures  of  the  multipli- 
cand, casting  out  the  9's  and  setting  the  excess  at  the  right. 
Proceed  in  the  same  manner  with  the  multiplier,  setting  the 
excess  under  that  of  the  multiplicand.  Multiply  these  excesses 
together  and  cast  the  9's  out  of  the  result.  Then  cast  out  the 
9's  in  the  original  product,  and,  if  the  work  is  correct,  the  last 
two  excesses  will  agree.  Although  this  is  not  always  an  abso- 
lute test  of  the  correctness  of  a  result,  it  is  sufficiently  so  for 
common  purposes. 

Ex.  2.  Multiply  23045  by  70800. 

Proof. 
23045  5  Excess. 

70800  _6        " 

184360  30  )  3  " 

161315  ( 


Product,  1631586000  •}  3  " 

Examples. 

3.  Multiply  405678  by  34006. 

4.  Multiply  38674506  by  30080. 

5.  Multiply  46923000  by  46702. 

6.  Multiply  83400607  by  33000. 

7.  Multiply  843464  by  30706. 

8.  Multiply  708000  by  4700. 

9.  How  many  feet  would  a  horse  travel  in  109  days  at  the 
rate  of  35  miles  per  day  ?     (A  mile  contains  5280  feet.) 

10.  How  much  can  508  men  earn  in  65  days,  if  each  man 
receives  3  dollars  per  day  ? 


DIVISION.  23 


DIVISION. 


ART.  10.  Ex.  1.  Divide  2920464  by  60843. 
60843)2920464(48  Quotient. 
243372 


486744 
486744 

Suggestion. — Make  6  your  trial  divisor  and  29  your  first 
trial  dividend.     The  second  trial  dividend  is  48. 
Ex.  2.  Divide  2406874  by  30400. 

304  00)24068  74(79  Quotient. 
2128 
2788 
2736 

5274  Remainder. 

Examples. 

3.  Divide  304608  by  304. 

4.  Divide  6743207  by  6200. 

5.  Divide  340068  by  27. 

6.  Divide  84306200  by  308000. 

7.  Divide  8408  by  24. 

8.  Divide  345602  by  18.  * 

9.  Divide  4060703  by  33. 
10.  Divide  412304  by  30300. 


CONTRACTIONS  IN  MULTIPLICATION  AND 
DIVISION. 

ART.  11.  There  are  abbreviated  methods  of  multiplying 
and  dividing  numbers,  which  the  expert  accountant  can  often 
use  with  great  advantage.  With  a  little  practice  a  person 
may  readily  multiply  by  two,  three,  or  even  more  figures,  at  a 
single  operation.  The  process  of  division,  may  be  abbreviated 
in  a  similar  though  less  practical  manner.  Many  of  these 


24  DIVISION. 

methods,  together  with  their  explanations,  are  too  complex  for 
insertion  here.  The  living  teacher  can  best  present  such  pro- 
cesses. Unless  the  student  is  made  familiar  with  them,  they 
are  of  no  practical  importance. 

ART.  12.  When  the  multiplier  is  14,  15,  16,  etc. 
Ex.  1.  Multiply  3425  by  15. 
Operation. 
3425  x 15 
17125 

51375  Product. 

Remark. — It  is  not  necessary  to  put  down  any  part  of  the 
operation.     The  result  may  be  written  at  once  by  the  following 

RTJLE. 

Multiply  by  the  unit's  figure,  adding,  after  the  unit's  place, 
the  figures  of  the  multiplicand. 

Examples. 

2.  Multiply  34809  by  13. 

3.  Multiply  4876  by  18. 

4.  Multiply  369403  by  17. 

5.  Multiply  369403  by  13. 

6.  Multiply  369403  by  16. 

7.  Multiply  369403  by  15. 

8.  Multiply  369403  by  14.      , 

ART.  13.  When  the  multiplier  is  31,  41,  51,  etc. 
Ex.  1.  Multiply  3425  by  51. 

Operation. 
3425x41 
13700 

140425  Product. 

RULE. 

Multiply  by  the  ten's  figure  and  add  the  p*  )duci  to  the 
proper  orders  of  the  multiplicand. 

Examples. 

2.  Multiply  3486  by  71. 

3.  Multiply  864  by  51. 


DIVISION.  25 

4.  Multiply  86047  by  41. 

5.  Multiply  38967  by  91. 

ART.  14.  When  the  multiplier  consists  of  two  figures,  the 
product  may  be  written  at  once. 

Ex.  1.  Multiply  675  by  56. 

675x56=37800. 

Explanation. — The  process  is  based  upon  the  fact  that 
units  multiplied  by  units  give  units,  tens  by  units  tens,  tens  by 
tens  hundreds,  hundreds  by  units  hundreds,  hundreds  by  tens 
thousands,  etc. 

We  first  multiply  5  units  by  6  units =30  units =3  tens  and 
0  units.  Write  0  units.  Multiply  7  tens  by  6  units =42  tens, 
and  add  3  tens,  (received  from  the  units,) =45  tens,  and  to  this 
add  5  tens  by  5  units =25  tens,  which  gives  70  tens =7  hun- 
dreds and  0  tens.  Write  0  tens. 

Multiply  6  hundreds  by  6  units =36  hundreds,  and  add  the 

7  hundred,  received  from  the  tens,  which  gives  43  hundreds. 
Then  multiply  the  5  tens  by  7  tens =35  hundreds,  and  add  43 
hundreds =78  hundreds =7  thousands  and  8  hundreds.     Write 

8  hundreds.     Multiply  6  hundreds  by  5  tens =30  thousands, 
and  add  the  7  thousands  received  from  hundreds =37  thou- 
sands.    Write  37  thousand.     The  product  is  37800. 

Examples. 

2.  Multiply  38765  by  34.     By  45. 

3.  Multiply  68753  by  48.     By  84. 

4.  Multiply  23086  by  96.     By  69. 

5.  Multiply  6784  by  37.     By  73. 

6.  Multiply  8745  by  43.     By  34. 

7.  Multiply  6321  by  98.     By  89. 

ART.  15.  When  the  multiplier  is  a  convenient  part  of  10, 
100,  1000,  etc. 

RULE. 

Multiply  ~by  10,  100,  1000,  etc.  (by  annexing  ciphers)  of 
which  the  multiplier  is  a  party  and  take  the  same  part  of  the 
product. 


26  DIVISION. 

Ex.  1.  Multiply  357  by  33}. 
Operation. 
3)35700 

~TT900  Product. 

Explanation.— Since  33 }  is  one  third  of  100,  33J  times  357 
must  equal  i  of  100  times  357. 

Note. — The  following  are  some  of  the  convenient  parts 
often  occurring  :  of  10— 2},  3J ;  of  100— 12},  16},  25,  33},  50 ; 
of  1000—125,  166|,  250,  333},  500,  666|. 

Examples. 

2.  Multiply  528  by  3}.     By  2}. 

3.  Multiply  124860  by  12}.     By  16|. 

4.  Multiply  80648  by  25.     By  33}. 

5.  Multiply  10368  by  125.     By  166|. 
.6.  Multiply  62208  by  333}.     By  666}. 

ART.  16.  To  divide  by  a  convenient  part  of  10,  100,  1000, 
etc. 

RTJJL.E. 

Multiply  by  the  quotient,  found  by  dividing  10,  100,  1000, 
etc.,  (as  the  case  may  be)  by  the  given  divisor,  and  divide  the 
result  by  10,  100,  1000,  etc. 
Ex.  1.  Divide  850  by  16|. 

Operation. 
850 
_6 

51.00    Ans.  51. 

Explanation. — Since  100  is  6  times  16  f,  100  is  contained 
as  many  times  in  6  times  a  given  number  as  16|  is  in  the 
number  itself. 

32  x  a  m.  pies. 

2.  Divide  465  by  2}.     By  3}. 

3.  Divide  54604  by  12}.     By  16|. 

4.  Divide  8364  by  25.     By  33}. 

5.  Divide  64575  by  125.     By  500. 

6.  Divide  647500  by  166|.     By  333}. 

7.  Divide  2564  by  6}.     By  250. 


i 

FEDERAL     MONEY.  27 


FEDERAL    MONEY. 

ART.  17.  TABLE. 

10  mills  (m)  make  1  cent,  marked  ct. 
10  cents  "     1  dime,       "     d. 

10  dimes  "     1  dollar,      «     $ 

10  dollars         "     1  Eagle,     "     E. 

E.     $       d.       ct.         m. 
1=10=100=1000=10000 

1=  10=  100=  1000 

1=     10=     100 

1=       10 

Remark. — Dimes  and  eagles  are  not  mentioned  in  ordinary 
business  transactions.  In  writing  dollars  and  cents  together, 
a  point,  called  the  separatrix  ( . ),  is  placed  between  the  dollars 
and  cents  ;  and,  since  cents  occupy  two  places,  the  first  figure 
at  the  right  of  cents  is  mills.  It  is  not  customary  to  separate 
cents  and  mills. 

Examples. 

1.  How  many  mills  in  28  cents  ?     In  37}  cents  ? 

2.  How  many  cents  in  15  dimes  ?     In  16}  dimes  ? 

3.  Keduce  $12.50  to  mills. 

4.  Change  $90  to  mills. 

5.  How  many  cents  in  2  eagles,  5  dollars,  and  8  dimes  ? 

6.  Reduce  4360  cents  to  dollars. 

7.  Add  the  following:  $9.60,  $12.70,  $45.37},  $.06,  $1.50, 
$4.98,  $68.33, '$8.39,  $60,  and  $.80. 

8.  Sold  a  carnage  for  $120.75,  a  horse  for'  $90.60,  a  har- 
ness for  $15.60,  and  a  saddle  for  $13.12}  ;    what  was  the 
amount  received  ?  Ans.  $240.075. 

9.  From  $108  take  12}  cents.  Ans.  $107.875. 

10.  Bought  a  barrel  of  flour  for  $6.37},  and  sold  it  for 
$5.87}  ;  what  did  I  lose  ?  Ans.  $.50. 

11.  Bought  a  house  and  lot  for  $1500.     Paid  $40  for  a 
front  fence,  $110.90  for  painting  house,  $9.75  for  fruit  trees, 


28  BILLS. 

and  $15  for  other  improvements.     I  then  sold  the  property  for 
$1800.     What  did  I  gain  ? 

12.  What  will  be  the  cost  of  45  barrels  of  flour  at  $5.80 
per  barrel  ? 

13.  What  will  80  bushels  of  coal  cost  at  15  cents  per  bushel  ? 

14.  What  will  be  the  cost  of  60  bushels  of  wheat  at  $1.12i 
per  bushel ;  146  bushels  of  corn  at  66 1  cents  a  bushel ;  and  45 
bushels  of  oats  at  25  cents  a  bushel  ? 

15.  How  many  bushels  of  coal  at  12  £  cents  a  bushel  can  be 
bought  for  $125  ? 

Suggestion. — The  dividend  and  divisor  must  be  reduced  to 
the  same  denomination.  Change  both  to  mills.  125. 000 -r- 
.125=1000.  Ans.  1000  bushels. 

16.  How  many  pounds  of  butter  at  16  cents  per  pound 
must  be  given  for  15  barrels  of  flour  at  $8  per  barrel  ? 

17.  How  many  barrels  of  flour  at  $5.62|  per  barrel  can  be 
bought  for  $225  ?  Ans.  40  barrels. 

18.  How  many  half-dimes  would  it  take  to  pay  for  16  cows 
at  $16.37i  per  head  ? 

19.  A  drover  bought  105  head  of  cattle  at  $57  per  head. 
He  paid  for  their  pasturage  one  month  $250,  and  then  sold 
them  at  $60  per  head.     What  did  he  gain  by  the  transaction  ? 

Ans.  $65. 


BILLS. 

ART.  18.  A  Bill  of  Goods,  or  simply  a  Bill,  is  a  written 
statement  of  goods  sold  and  their  prices. 

It  contains  the  time  and  place  of  the  transaction  and  the 
names  of  the  parties. 

A  bill  is  drawn  against  the  purchaser,  and  in  favor  of  the 
merchant  or  seller. 

A  bill  is  receipted  by  writing  the  words  Eeceived payment  at 
the  bottom  and  affixing  the  seller's  name.  A  bill  may  be  receipted 
by  a  cl  rk,  agent,  or  any  authorized  person,  as  in  bills  2  and  3. 

When  sales  are  made  at  different  times,  the  dates  of  the 
several  transactions  may  be  written  at  the  left. 


BILLS.  29 

A  bill  presenting  a  debit  and  credit  account  between  the 
parties  and  the  balance  due,  may  be  written  as  in  bill  7. 

If  the  party  against  whom  the  bill  is  drawn  is  not  able  to 
pay  it  when  presented,  he  may  acknowledge  the  same  by  giving 
a  due-bill.  This  will  prevent  all  subsequent  dispute  as  to  the 
correctness  of  the  claim.  A  bill  may  be  receipted  by  means  of 
a  due-bill,  as  in  bills  4  and  5. 

1.  CLEVELAND,  July  1,  1859. 

MB.  JOHN  COOK, 

Bought  of  Samuel  Bliss. 

15  Ibs.  Kio  Coffee,    .  .  .  @  16c.  .  $2.40 

50  Ibs.  W.  I.  Sugar,  .  .  @  8ic.  .        4.25 

36  Ibs.  Pearl  Starch,  .  .  @  12ic.  .        4.50 

8  gals.  Molasses,       .  .  .  @  40c.  .        3.20 

90  Ibs.  Butter  Crackers,  .  .  @  9c.  .         8.10 

45  Ibs.  Picnic  Crackers,  .  .  @  lie.  .        4.95 


Keceived  payment,  SAML.  BLISS. 

BUFFALO,  Jan.  1,  1860, 

PETER  HIND, 

1859.  Bought  of  James  Fink  &  Co. 

July  15.  9  yds.  Silk,  .     @  $0.95    .      ' 

"      "    8  yds.  Kibbon,    .        .        .     @      .45    . 

"      "    12  yds.  Muslin,  .        .         .     @      .15    . 
Sept.    9.  3  yds.  Cassimere,         .        .     @    1.75    . 

"      "    2i  yds.  Broadcloth,     .        .     ©    4.50    . 

"      "    6  yds.  Doeskin,  .         .        .     @    1.12i  . 

"      "    1  Cravat,  .     ©    1.25    . 

Oct.    15.  4  prs.  Boots,       .        .        .     @    5.20    . 

"      "    2  doz.  Hose,  .     ©    2.40    . 

"      "    i  doz.  Sleeve  Buttons,         .     @      .48    . 

"      "    3i  yds.  Linen,     .         .         .     ©      .60    . 
Nov.  30.  li  doz.  Collars,  .  .     @    2.25    . 

"      "    2  doz.  Handkerchiefs,          .     ©    1.40    . 

"     "    3  Vests,      .        .        .        .     ©    2.40    .      __ 

1,797765 

Received  payment,  JAMES  FINK  &  Co. 

per  SMITH. 


it       it 

1C         it 


30  BILLS. 

3.  NEW  YORK,  Jan.  1,  1859. 

MB.  JOHN  SMITH, 

To  Hurd  &  Brothers,  Dr. 
1858. 

Aug.  20.  To  12  yds.  Broadcloth,       .     @  $3.50  . 

16  yds.  Cassimere,         .     @    1.12  . 

17  yds.  Drilling,    .        .     @      .11  . 
Sept.  25.    "  12  doz.  Spools  On.  Thread,  ©      .60  . 

"     "     "  7  yds.  Gingham,    .        .     ©      .25    . 
"     "     "  34  yds.  Fine  Muslin,      .     ©      .18    . 
"     "     "  5  yds.  Eed  Flannel,       .    ©      .62J  . 
"•    "     "  21  yds.  Silk  Velvet        .     ©    400    . 
Oct.     9.     "  12  gross  Shirt  Buttons,     ©      .75    . 
15  doz.  Wool  Hose,       .    ©    3.00    . 
"  3  prs.  Kid  Gloves,         .    ©    1.25    . 
"     "     "  2  doz.  Linen  Napkins,  .     ©    2.40    . 
"     "     "  2  doz.  Shirt  Bosoms,     .     ©    4.80    . 
Nov.    1.     "  11  yds.  Drilling,    .        .     ©      .10    . 
;<  5  yds.  Jean,  .        .        .     ©      .75    . 
"  2  Silk  Kdks.,        .        .    ©    1.00    . 
«  12i  yds.  Vel.  Kibbon,    .     ©      .20    .      _ 

$171.485 
Eeceived  payment, 

JOHN  STILL, 
for  HUBD  &  BROTHEBS. 


4.  CHICAGO,  July  1,  1859. 

JOSEPH  CAMP, 

To  Geo.  W.  Colburn,  Dr. 
1859. 

Apr.  3.  To  3  doz.  Scythes,         .        .     ©  $9.00    . 

"  8.    "  li  doz.  Hoes,  .    ©    5.00    . 

Mayl.    a  6  doz.  Kakes,  .     ©    1.75    . 

$45XX) 

Keceived  payment  by  due-bill, 
July  15,  1859.  GEO.  W.  COLBUBN. 


(C       ((       a 
tt 


"      " 


BILLS.  31 

5^  CINCINNATI,  June  20,  1859. 

AMOS  KENT,  ESQ., 

To  W.  B.  Cook  &  Co.,  Dr. 

To  1  doz.  Webster's  Unabridged  Dictionary,  @  $50.00 
"  12  doz.  Kobinson's  Arithmetic,  .  .  @  9.00 
"  5  doz.  Sanders'  Fifth  Headers,  .  .  @  7.20 
"  9  doz.  Wells's  Grammar,  .  @  3.00 

"  2^  doz.  Small  Testaments,  .     @      1.20 

$224 
Julyl.  Settled  by  due-biU, 

W.  B.  COOK  &  Co. 


6. 
MR.  J.  H.  POE, 

1859. 

May     3.  75  Ibs.  Sugar, 

"     "  9  Ibs.  Tea,      . 

"     "  21  gals.  Golden  Syrup,  . 

June    1.  10  Ibs.  Spice, 

"  12  Ibs.  Pepper,       . 

"  12  Ibs.  Ginger,       . 

"  15  Ibs.  Coffee, 

10.  20  Ibs.  Dried  Apples,     . 

"  18  Ibs.  Dried  Peaches,    . 

"  2  bu.  Onions, 

15.  13  Ibs.  Mackerel,    . 

18.  9  Ibs.  Smoked  Herrings, 

20.  25  Ibs.  Kice,  . 

"  12  Ibs.  Dried  Beef, 

"  5  Sacks  Table  Salt, 

"  5  bu.  Corn  Meal,   . 

27,  17  Ibs.  Soda  Crackers,   . 

Keceived  payment, 


PORTSMOUTH,  July  1,  1859. 

Bought  of  Wm.  Miller. 

.  @  6jc  . 

.  @  65c  . 

.  @  70c  . 

.  @  20c  . 

.  @  25c  . 

'    .  @  18c  . 


@  lOc 
@  12|c 
@  80c 
@8c 
@  20c 
@  5c 
@  12ic 
@  20c 
@  80c 
@  9c 


$52.24 
WM.  MILLER. 


32 


GREATEST     COMMON     DIVISOR. 


7. 
KEED  & 

1859. 
July    7. 


SPRY, 


ST.  Louis,  Jan.  1,  1859. 

To  Hall,  Smith  &  Co.,  Dr. 


1C  CC 

CC  CC 

"  20. 

CC  CC 

CC  CC 


To  15  yds.  Cambric,  .  @  9c  . 

"    50  yds.  Print,     .  .  @  12ic  . 

"    6  yds.  Cassimere,  .  @  $1.60 

"   33  yds.  Sheeting,  .  @  lie  . 

"    6J  yds.  Broadcloth,  .  @  $4.37^  . 

"   3  yd.  Velvet,      .  .  @  3.00  . 

Aug.  30.    "   20  yds.  French  Print,  @  17c  . 

"     "     "15  yds.  Lyonese,  .  @  70c  . 

Or. 

Sept.    1.  By  40  bu.  Coal,       .  .  @         lie  . 

"      9.    "    6  Cords  of  Wood,  .  @  $  3.00  . 

Oct.   20.    "    Cash,  .  @    16.00  . 

Nov  25.    "   8  Days'  Labor,  .  .  @      1.50  . 

Balance  due,    ..... 
Keceived  payment, 

HALL,  SMITH  & 
per  HIBBS. 


$50.40 
$15.02 

Co, 


GREATEST    COMMON    DIVISOR. 

ART.  19.  Integers,  or  whole  numbers,  are  divided  into  two 
classes,  prime  and  composite. 

A  prime  number  can  be  exactly  divided  only  by  itself  and 
unity  ;  as  2,  3,  5,  7,  11,  etc, 

A  composite  number  can  be  exactly  divided  by  other  num- 
bers besides  itself  and  unity  ;  as  4,  9,  21,  etc. 

The  factor  of  a  number  is  one  of  two  or  more  numbers 
which  multiplied  together  will  produce  the  given  number. 
The  factors  of  12  are  2,  3,  4,  6,  1,  and  12,  since  each  of  these 
numbers  multiplied  by  another  will  produce  12. 


GREATEST     COMMON     DIVISOR.  33 

The  prime  factors  of  a  number  are  all  the  prime  numbers 
which  multiplied  together  will  produce  the  given  number. 
The  prime  factors  of  12  are  1,  2,  2  and  3. 

Two  or  more  numbers  are  said  to  be  prime  tvith  respect  to 
each  other  when  they  have  no  common  factor  ;  as  8,  21,  and  35. 

The  divisor  of  a  number  is  any  number  that  will  exactly 
divide  it.  Thus  4  is  a  divisor  of  12,  16,  and  24. 

Note.  —  Every  factor  is  a  divisor  and  vice  versa. 

A  common  divisor  of  two  or  more  numbers  is  any  number 
that  will  exactly  divide  each  of  them.  Thus  4  is  a  common 
divisor  of  16,  32,  and  64. 

The  greatest  common  divisor  of  two  or  more  numbers  is  the 
greatest  number  that  will  exactly  divide  each  of  them.  Thus 
16  is  the  greatest  common  divisor  of  16,  32,  and  64. 

ART.  20.  To  find  the  greatest  common  divisor  of  two  or 
more  numbers. 

Ex.  1.  What  is  the  greatest  common  divisor  of  63  and  105  ? 

Explanation.  —  3  and  7  are  the  only 

ro  J?SToMET7OD'  factors  common  to  63  and  105,  hence 

Oo  —  O  X  o  X  / 

105=3x5x7  ™iey  are  the  only  common  divisors, 

.     3x7=21.  Ans.        an(^  their  product  must  be  the  great- 

est common  divisor. 
Explanation.  —  That  the  last  divisor  is 

SECOND  METHOD.  ,  .  . 

63)105(1  the  greatest  common  divisor  is  evident  from 

63  the  following  analysis  : 

42)63(1  42=21x2;    hence  21   will  divide  42. 

63=42  +  21  =  21  x  2  +  21x1  =  21x3  ; 

hence  21  wm  divde  63. 


21  105  =  63+42  =  21x3+21x2  =  21x5; 

hence  will  also  divide  105. 

IR-TILE. 

Resolve  the  numbers  into  their  prime  factors.  The  pro- 
duct of  the  factors  common  to  all  the  numbers  will  be  the  great- 
est common  divisor.  Or, 

Divide  the  greater  number  ~by  the  less  ;  the  less  number  by 
the  first  remainder;  the  first  remainder  by  the  second  remain- 

3 


34  LEAST     COMMON     MULTIPLE. 

der;  the  second  remainder  by  the  third,  and  so  on  until  noth- 
ing remains.  The  last  divisor  will  be  the  greatest  common 
divisor. 

Note. — The  greatest  common  divisor  is  chiefly  used  in  re- 
ducing fractions  to  their  lowest  terms.  See  Art.  24. 

Find  the  greatest  common  divisor  of  the  following  num- 
bers : 

2.  56  and  98. 

3.  69  and  161. 

4.  168  and  392. 

5.  85  and  136. 

6.  126  and  294. 

7.  148  and  296. 

8.  16,  32,  and  86. 

Suggestion. — First  find  the  greatest  common  divisor  of  two 
of  the  numbers  ;  then  use  the  greatest  common  divisor  of  these 
two  numbers  as  a  new  number,  and  find  the  greatest  common 
divisor  of  it  and  the  third  number. 
9.  92,  138,  and  161, 

10.  2048  and  2560. 


LEAST    COMMON    MULTIPLE. 

ART.  21.  A  multiple  of  a  number  is  any  number  it  will 
exactly  divide  ;  thus  24  is  a  multiple  of  6. 

A  common  multiple  of  two  or  more  numbers  is  any  number 
each  of  them  will  exactly  divide.  Thus  96  is  a  common  mul- 
tiple of  8,  12,  16,  and  24. 

The  least  common  multiple  of  two  or  more  numbers  is  the 
least  number  each  of  them  will  exactly  divide.  Thus  48  is  the 
least  common  multiple  of  8,  12,  16,  and  24. 

It  is  evident  that  the  multiple  of  a  number  must  contain 
all  its  prime  factors,  otherwise  it  can  not  contain  the  number 
itself.  It  follows  from  this,  that  a  common  multiple  of  two 
or  more  numbers  must  contain  all  the  prime  factors  of  each 


LEAST     COMMON     MULTIPLE.  35 

of  the  numbers,  and  that  the  least  common  multiple  of  two 
or  more  numbers  must  contain  all  the  prime  factors  only 
the  greatest  number  of  times  they  are  found  in  any^  of  the 
numbers. 

ART.  22.  To  find  the  least  common  multiple  of  two  or 
more  numbers. 

Ex.  1.  What  is  the  least  common  multiple  of  21,  63,  108  ? 

Explanation. — The  mul- 

FIEST  METHOD.  tiple  of  108  must  contain 

nQ~o  *  o  ,  v  the  factor  3  three  times  and 

—       XOX/  -i        /»  r»          •  i 

10§ =3x3x3x2x2  *ne *actor  2  twice ;  the mul- 

3x3x3x4x  7=756  Ans.     ^P^e  °f  ^3  must  contain  the 

factor  3  at  least  twice  and 

7  once  ;  the  multiple  of  21  must  contain  the  factor  3  at  least 
once  and  7  once.  It  is  evident  that  a  number  that  contains 
the  factor  3  three  times,  the  factor  7  once,  and  the  factor  2 
twice,  is  the  least  common  multiple  of  21,  63,  and  108. 

R  UJL.E. 

fiesolve  each  of  the  given  numbers  into  its  prime  factors. 
The  product  of  the  different  factors,  each  factor  being  taken 
the  greatest  number  of  times  it  occurs  in  any  of  the  number  sy 
will  be  the  least  common  multiple. 

Note. — This  method  is  not  often  used. 

Explanation. — It  is  evident  that 

SECOND  METHOD.  by  this  method  the  same  result  is 

obtained  as  by  the  former  method, 

viz  :  the  greatest  number  of  times 

o)l—  3—  36  eacfa  prime  factor  enters  in  any  of 

the   numbers.      756   contains   the 

3x3x12x7=756  ^4rcs.     f    ,     Q  ,,       ,.         0,    .          ,  „ 

factor  3  three  tunes,  2  twice,  and  7 

once  (12=2x2x3). 

E.TJLE. 

Arrange  the  numbers  on  a  horizontal  line,  divide  by  any 
prime  number  that  ivill  exactly  divide  two  or  more  of  the  num- 
bers, and  write  the  quotients  and  undivided  numbers  in  a  line 


36  COMMON     FRACTIONS. 

beneath.  Divide  this  line  of  numbers  in  the  same  manner  as  the 
first ,  and  so  on  until  no  prime  number  will  exactly  divide  two 
numbers.  The  product  of  all  the  divisors  and  undivided  num- 
bers will  be  the  least  common  multiple  required. 

Find  the  least  common  multiple  of  the  following  num- 
bers : 

2.  8,  12,  16,  24,  and  36. 

3.  9,  15,  21,  and  75. 

4.  3,  8,  9,  15,  and  32. 

5.  17,  34,  68,  and  5. 

6.  8,  12,  16,  35,  and  84. 

7.  3,  4,  5,  6,  8,  10,  and  12. 

8.  5,  4,  6,  9,  and  7. 

9.  7,  8,  49,  98,  and  168. 

10.  |,  f,  |,  and  f . 

Suggestion. — Reduce  fractions  to  a  common  denominator, 
and  then  find  the  least  common  multiple  of  their  numerators. 

11.  2|,  5,  3 J,  and  4j. 


COMMON    FRACTIONS. 

ART.  23.  If  a  unit  or  a  body,  as  an  apple,  an  orange,  etc.,  be 
divided  into  four  equal  parts,  one  of  these  parts  is  one-fourth  of 
the  whole  ;  two,  two-fourths  ;  three,  three-fourths  ;  four,  four- 
fourths — which  are  respectively  written  1,  f ,  f ,  f .  These  ex- 
pressions are  called  fractions  ;  the  number  above  the  line  being 
called  the  numerator,  and  the  number  below  the  line  the  de- 
nominator. Hence,  "a fraction  is  an  expression  for  one  or 
more  of  the  equal  parts  of  a  unit." 

It  is  evident  that  the  denominator  shows  into  how  many 
equal  parts  the  unit  has  been  divided  ;  the  numerator,  how 
many  of  these  equal  parts  are  taken.  The  numerator  and  de- 
nominator are  called  terms  of  the  fraction. 

A  fraction  may  also  be  regarded  as  an  expressed  division, 
the  numerator  being  the  dividend  and  the  denominator  the 


COMMON     FRACTIONS.  37 

divisor.  3-7-4  may  also  be  written  •£  ;  the  value  of  the  frac- 
tion being  the  quotient.  4  is  contained  in  3  three-fourths  of  a 
time. 

A  common  or  vulgar  fraction  is  one  in  which  both  terms 
are  written  ;  as  £,  -f ,  T\,  etc. 

Common  fractions  are  divided  into  three  classes,  simple, 
compound,  and  complex. 

A  simple  or  single  fraction  has  but  one  numerator  and  one 
denominator,  each  being  a  whole  number  ;  as  £  and  J. 

A  compound  fraction  consists  of  two  or  more  simple  frac- 
tions connected  by  the  word  of ;  as  |  of  £,  and  f  of  -f  of  2|. 

A  complex  fraction  has  a  fraction  for  one  or  both  of  its 

terms  ;  as  I,  1,  and  5. 

3J     7>  3 

4 

Simple  fractions  are  divided  into  proper  and  improper. 

A  proper  fraction  is  one  whose  numerator  is  less  than  its 
denominator  ;  as  |,  J,  etc. 

An  improper  fraction  is  one  whose  numerator  is  equal  to 
or  greater  than  its  denominator  ;  as  £•  and  | . 

A  mixed  number  is  composed  of  a  whole  number  and  a 
fraction  ;  as  12  J,  16|,  etc.  The  fraction  is  added  to  the  whole 
number,  12|  being  the  same  as  12  +  |. 

It  is  evident  from  the  very  nature  of  a  fraction  that  both  of 
its  terms  may  be  multiplied  or  divided  by  the  same  number 
without  changing  its  value. 

The  value  of  a  fraction  may  be  increased,  1.  By  adding  to 
its  numerator.  2.  By  multiplying  its  numerator.  3.  By  sub- 
tracting from  its  denominator.  4.  By  dividing  its  denominator. 

The  value  of  a  fraction  may  be  decreased,  1.  By  adding  to 
its  denominator.  2.  By  multiplying  its  denominator.  3.  By 
subtracting  from  its  numerator.  4.  By  dividing  its  numerator. 

ART.  24.  To  reduce  a  fraction  to  its  lowest  terms. 

Ex.  1.  Reduce  f  £  to  its  lowest  terms. 

4)tA=2)T6T-3?  Ans.     Or,  8)f*=^  Ans. 

Explanation. — Since  both  terms  of  a  fraction  may  be  di- 
vided by  the  same  number  without  changing  its  value,  divide 
both  numerator  and  denominator  by  4.  The  result  is  /?. 


38  COMMON     FRACTIONS. 

Again,  divide  both  terms  of  this  fraction  by  2  ;  the  result  is  --J, 
which  can  not  be  reduced  lower,  since  no  number  greater  than 
1  will  divide  both  of  its  terms.  Or  divide  by  8,  the  greatest 
number  that  will  divide  both  terms  of  the  fraction  ;  the  result 

i«  3 

is  T. 

E.TJ3L.E. 

Divide  both  terms  of  the  fraction  by  any  number  that  will 
divide  each  of  them  without  a  remainder,  and  proceed  until 
they  are  prime  to  each  other.  Or, 

Divide  both  terms  of  the  fraction  by  their  greatest  common 
divisor. 

E  x  am.  pies. 

2.  Reduce  f  f  to  its  lowest  terms. 

3.  Reduce  TW  to  its  lowest  terms. 

4.  Reduce  TVj  to  its  lowest  terms. 

5.  Reduce  TW  to  its  lowest  terms. 

6.  Reduce  Iff  to  its  lowest  terms. 

7.  Reduce  T\64  to  its  lowest  terms.  Ans.  f. 

8.  Reduce  T3/^-  to  its  lowest  terms.  Ans.  }f- 

9.  Reduce  f  iff  to  its  lowest  terms.  Ans.  -f. 
10.  Reduce  fWV  to  its  lowest  terms.                   Ans.  T4T. 
ART.  25.  To  reduce  a  fraction  to  higher  terms. 

Ex.  1.  Reduce  f  to  twelfths. 

1=  T\,  |=  '  x  ,3,=  _?_  AnSm     Or,  f  x  3=  T<V  Ans. 

Explanation.  —  Since  1  fourth  equals  3  twelfths,  3  fourths 
must  equal  3  times  3  twelfths,  which  is  9  twelfths.  Ans.  T\. 
Or,  since  both  terms  of  a  fraction  may  be  multiplied  by  the 
same  number  without  changing  its  value,  multiply  both  nu- 
merator and  denominator  by  3. 


es 


33  x  am  p  1 

2.  Reduce  f  to  sixty- thirds.  Ans.  f  J. 

3.  Reduce  T\  to  sixtieths.  Ans.  f  £. 

4.  Reduce  T\  to  fifty-sevenths. 

5.  Reduce  ¥8T  to  eighty-fourths. 

6.  Reduce  J  to  fifteenths. 


COMMON     FRACTIONS.  39 

7.  Reduce  -V~  to  twenty-sevenths. 

8.  Reduce  £,  f  ,  and  f  to  twenty-fourths. 

Ans.  |},  |i,  and  if. 

9.  Reduce  4,  f  ,  and  T3T  to  seventieths. 

10.  Reduce  ^  f  ,  f  ,  and  T<V  to  forty-eighths. 

ART.  26.  To  reduce  an  improper  fraction  to  a  whole  or 
mixed  number. 

Ex.  1.  Reduce  -M-  to  a  mixed  number. 
49-^5=9f  Ans. 

Explanation.  —  Since  5  fifths  make  1,  there  will  be  |s  many 
ones  in  49  fifths  as  5  is  contained  times  in  49,  which  is  9}. 

RULE. 

Divide  the  numerator  by  the  denominator. 

Examples. 

2.  Reduce  -1/-  to  a  mixed  number. 

3.  Reduce  -\5-  to  a  mixed  number. 

4.  Reduce  f  J  to  a  whole  number. 

5.  Reduce  -W-  to  a  mixed  number. 

6.  Reduce  JTy-  to  a  mixed  number. 

7.  Reduce  -V/-  to  a  mixed  number.  -^ws.  3/g-. 

8.  Reduce  -\5-  to  a  whole  number.  Ans.  25. 

9.  Reduce  -J-J-  to  a  mixed  number.  -4ws.  5T2T. 
10.  Reduce  ^-f  ^  to  a  mixed  number.                  Ans.  17|. 
ART.  27.  To  reduce  a  whole  or  mixed  number  to  an  im- 

proper fraction. 

Ex.  1.  Reduce  5f  to  an  improper  fraction. 


_a_3 


Explanation.  —  Since  there  are  4  fourths  in  1,  in  5  there 
are  5  times  4  fourths  =20  fourths,  and  20  fourths  +  3  fourths  = 
23  fourths.  Ans.  -V- 


Multiply  the  whole  number  by  the  denominator  of  the  frac- 
tion, to  the  product  add  the  numerator,  and  under  the  result 
place  the  denominator. 


? 


40  COMMON     FRACTIONS. 

Examples. 

2.  Keduce  4A"S  to  an  improper  fraction. 

3.  Keduce  SyVj  to  an  improper  fraction.         Ans.  f 

4.  Keduce  56  £  to  an  improper  fraction. 

5.  Reduce  1236?97  to  an  improper  fraction.   Ans.  --V/—- 

6.  Reduce  5Tf  ¥  to  an  improper  fraction. 

7.  Reduce  23r9¥  to  an  improper  fraction.         Ans.  -3Ty. 

8.  Reduce  133Tf  to  an  improper  fraction. 

9.  Reduce  563f  to  an  improper  fraction.        Ans.  &  -M-2-. 
lO.^Reduce  8006  ff  to  an  improper  fraction. 

Ans.  laa-Mi. 

11.  Reduce  24  to  fourths.  Ans.  Y- 

12.  Reduce  35  to  twentieths.  Ans.  -yy1- 

13.  Reduce  312  to  twelfths. 

14.  Reduce  19  to  twenty-fifths. 

15.  Reduce  1008  to  ninths. 

ART.  28.  To  reduce  compound  fractions  to  simple  ones. 
Ex.  1.  Reduce  f  of  |  to  a  simple  fraction. 

fnf   5  _  4^5  -  20        A  M  n 
oi  g  __---—  3  w  j±ns. 

Explanation.  —  1  of  J  is  J-0-,  and  1  of  |  is  5  times  ^\  or  /0, 
and  if  |  of  |  is  /0,  f  of  |  is  4  times  /„?  or  1^=1  Ans.  This 
is  in  effect  multiplying  the  numerators  together  and  also  the 
denominators. 


Multiply  the  numerators  together  for  the  numerator  of  the 
simple  fraction,  and  the  denominators  together  for  its  denom- 
inator. 

Note.  —  If  there  are  whole  or  mixed  numbers,  first  reduce 
them  to  improper  fractions. 

Examples. 

2.  Reduce  |  of  f  of  f  to  a  simple  fraction.          Ans.  -r\. 

3.  Reduce  3^  of  2|  of  T\  to  a  simple  fraction.     Ans.  2j. 

4.  Reduce  2£  of  1^  of  f  to  a  simple  fraction. 

5.  Reduce  f  of  J  of  2i  to  a  simple  fraction. 

6.  Reduce  f  of  1|  of  -f  of  2i  to  a  simple  fraction.  Ans.  }. 

7.  Reduce  f  of  6  to  a  simple  fraction. 

8.  Reduce  f  of  2£  of  3  to  a  simple  fraction. 


COMMON     FRACTIONS.  41 

CANCELLATION. 

ART.  29.  The  above  operations  may  be  abbreviated  by  in- 
dicating the  multiplications  to  be  performed,  and  then  cancel- 
ling the  factors  common  to  both  terms,  as  shown  in  the  follow- 
ing examples. 

Ex.  1.  Keduce  £  of  £  of  4  of  2i  to  a  simple  fraction. 

2    2 

$x$x0x#     4 
4x0xtfx3=3  =  13  Ans' 

3 
2.  Reduce  f  of  £  of  f  of  f  of  .;  of  l£  to  a  simple  fraction. 


3 

.  —  1  remains  as  a  factor  in  the  numerator. 

3.  Reduce  \  of  4i  of  T9T  of  J-  to  a  simple  fraction. 

4.  Reduce  f  of  2ff  of  •£-*  of  f  to  a  simple  fraction. 

Ans.  T7T. 

5.  Reduce  |  of  |  of  f  of  T\  of  12  f  to  a  simple  fraction. 

Ans.  3f. 

6.  Reduce  f  of  3  £  of  T6T  of  }i  of  r7j  of  7f  to  a  simple  fraction. 
Remark.  —  The  principle  of  cancellation  may  often  be  used 

with  great  advantage.  Whenever,  to  obtain  a  certain  result, 
several  multiplications  and  divisions  are  to  be  performed,  indi- 
cate the  operations  and  cancel  the  factors  common  to  the  mul- 
tipliers and  divisors. 

7.  Divide  the  product  of  24,  16|,  8,  33i  by  12,  16|,  and  66|. 

t 


8.  Multiply  48,  32,  5280  and  27  together,  and  divide  the 
result  by  16,  264,  54  and  6.  Ans.  160. 

9.  How  many  cords  of  wood  in  a  pile  144  feet  long,  12  feet 
high  and  3  feet  wide  ? 

109    3 

x  3 

=       Ans' 


42  COMMON     FRACTIONS. 

10.  Multiply  9,  8,  18,  45,  36,  90,  81  together  and  divide 
the  result  by  72,  180,  27,  24,  4  and  18.  Ans.  25TV 

ART.  30.  To  reduce  fractions  to  a  common  denominator. 

Ex.  1.  Reduce  f,  f,  f,  f  and  T7^  to  equivalent  fractions 
having  a  common  denominator. 

Solution.  First  Method. — It  is  evident  upon  a  little  in- 
spection that  each  of  the  fractions  can  be  changed  to  twenty- 
fourths.  According  to  Art.  24,  J  =  i£,  f  =  H>  f  =  f£,  ?  =  ££, 
and  T73  =  £J.  Hence  f,  f,  £,  f  and  T\  are  respectively  equal  to 
if?  if?  IT?  if  an<l  if?  fractions  having  a  common  denominator. 

Second  Method. — The  least  common  multiple  of  4,  8,  6,  3 
and  12  (denominators)  found  by  Art.  22,  is  24,  which,  being 
divided  by  4,  8,  6,  3  and  12  respectively,  give  the  multipliers 
by  which  both  terms  of  their  respective  fractions  are  to  be 
multiplied  3Xe  — 11  i^  —  n  5x4  —  20.  2j<_s_i6  and-^^_ 

4X6          247    8X3          24?    6X4  24?    3X8          24?  12X2 

if. 

KULE  FOR  SECOND  METHOD. — Find  the  least  common  mul- 
tiple of  the  denominators.  Then  divide  the  least  common  mul- 
tiple by  the  denominator  of  each  fraction  and  multiply  both 
of  its  terms  by  the  quotient. 

Note. — The  first  method  is  the  one  generally  used.  In  ordi- 
nary examples,  the  common  denominator  can  be  seen  at  a 
glance. 

t 

E  x  a  m.  pies. 

Reduce  the  following  fractions  to  equivalent  fractions  hav- 
ing a  common  denominator. 

2.     I,    f,    1,    TV,    JV. 

3.  |  and  ,V 
4-  t,  |,  i,  f. 

5.  |,  I,  I,  i- 

6.  i  of  l,2i,  |.  Ans.  f,-V-,f. 

7.  i  off,  f,2i. 

Q      i      i      i      i      i       i 
°*    "3?    4?  IT?  F?   ¥>   !!?• 

9.  !,  !,  f,  1- 


COMMON     FRACTIONS.  43 


ADDITION    OF    COMMON    FRACTIONS. 

ART.  31.  Ex.  1.  What  is  the  sum  of  f  ,  £  ,  £  and  J  ? 

|+t+t+»= 
H+H-Kfi+H==tt==3i 

Ex.  2.  Add  |  of  |,  f  of  -f  and  2i 

tof  }=f,  f  of  i=i52i 


=  W=  341 


RULE. 

Reduce  the  fractions  to  a  common  denominator;  then  add 
their  numerators,  and  under  their  sum  place  the  common  de- 
nominator. 

Notes.  —  1.  First  reduce  mixed  numbers  to  improper  frac- 
tions, and  compound  fractions  to  simple  ones. 

2.  The  integers  may  be  set  aside  and  subsequently  added 
to  the  sum  of  the  fractions. 

1C  x  a  m  pies. 

3.  Add  |,  f,  |  and  i.  Ans.  2jf. 

4.  Add  |  of  f  and  TV  Ans.  1/T. 

5.  Add  |,  f  and  f  Ans.  !}££. 

6.  Add  5i,  3f,  5|.  ^s.  14jf  . 

7.  Add  |  of  2J  and  f  of  2j.  -4w«.  2. 

8.  Add  1026ii,  1875|  and  5634  f.          Ans.  8536ff  f. 
Suggestion.  —  First  add  the  fractions. 

9.  Add  37i,  18f  ,  33i  and  81J.  Ans.  170|. 

10.  Add  |,  J»T  of  4i,  563f,  and  |  of  3f. 

11.  Add  i,  i,  J,  i  and  1. 

12.  Add  |,  f,  T\,  andf  ofl}. 

13.  Add  i,  i,  i,  i,  and  J. 

14.  Add  |  of  f  and  12i. 

15.  Add  105|  and  98TV 


44  COMMON     FRACTIONS. 

SUBTRACTION    OF    COMMON    FRACTIONS. 
ART.  32.  Ex.  1.  From  %  take  f . 

Ex.  2.  From  2  J  take  }  of  2. 

2i=f,  Jof  f=f 


RTJLE. 

Reduce  the  fractions  to  a  common  denominator;  then  sub- 
tract their  numerators,  and  under  the  result  place  the  common 
denominator. 

Note.  —  Mixed  numbers  may  be  subtracted  without  reducing 
them  to  improper  fractions. 

3.  Subtract  f  from  f  .  Ans.  TV 

4.  Subtract  T2T  from  f  . 

5.  From  1  of  f  take  f  of  T2T.  Ans.  //„. 

6.  From  f  of  f  take  1. 

7.  From  i  of  J  take  T\  of  J.  ^ws.  }  j. 

8.  From  820|  subtract  56}. 

820|,  A 


_ 

763}i  Ans. 
9.  From  250}  subtract  225f 

10.  From  993f  take  546|.  Ans.  446f 

11.  From  J  +  J  +  4-  take  f  of  f  +  T\  off.  Ans.  ||. 

12.  From  |  of  12  take  f  of  9. 

13.  From  1000  take  156|. 

14.  From  9  take  1  of  }. 

15.  From  56A-f  89|  take  5}  +  81TV 

16.  From  J'of  13  take  |  of  8. 

17.  From  3|  of  5  take  2j  of  7.  ^ws.  Ij. 

18.  From  4  of  42  take  f  of  48.  Ans.  16f. 

19.  From  f  of  19J  take  |  of  7f.  ^iw.  9}f 

20.  From  8751  take  599f 


COMMON     FRACTIONS.  45 


MULTIPLICATION    OF    COMMON    FRACTIONS. 

ART.  33.  To  multiply  a  fraction  by  a  whole  number. 
Ex.  1.  Multiply  T\  by  4. 

5     X4  -  20  -  5  -  1  2      Ama          Or  -  _  -  5  -  I2      /4'MC 

T2-        —  T¥—  3-  —  -"-3-  -AnS.       Ur?  —  —  _  3  _  1  j  ^TiS. 

Explanation.  —  4  times  T\  is  ff=f,  or  1|.  It  is  evident 
that  the  same  result  is  obtained  by  dividing  the  denominator 
by  4. 


Multiply  the  numerator  of  the  fraction  by  the  whole  num- 
ber, or  divide  the  denominator. 

2.  Multiply  /T  by  16.  Ans.  If. 

3.  Multiply  if  by  3.  Ans.  2f  . 

4.  Multiply  ff  by  9.  Ans.  6|. 

5.  Multiply  T|fF  by  25. 

ART.  34.  To  multiply  a  whole  number  by  a  fraction. 
Ex.  1.  Multiply  15  by  |. 
15xJ  =  -y.=lli  Ans.    Or,  15-^4=3£,  3fx3=llf  ^W5. 

Explanation.  —  Since  |  =  i  of  3,  f  times  15  is  \  of  3  times 
15,  or  45,  and  |  of  45=11^  Ans.  Or,  since  1  times  15  is 
15,  }  times  15  is  \  of  15—  3f,  and  |  times  15  is  3  times 
32=111  Ans. 

Ex.2.  Multiply  5280  by  |  . 

8)5280  5280 

660  _j? 


_ 

5  Or,  8)26400 


_ 
3300  Ans.  3300  Ans. 


Multiply  the  ivhole  number  by  the  numerator  of  the  frac- 
tion and  divide  the  product  by  the  denominator.  Or, 

Divide  the  whole  number  by  the  denominator  of  the  frac- 
tion and  multiply  the  quotient  by  the  numerator. 

3.  Multiply  56  by  f  .  Ans.  35. 


46  COMMON     FRACTIONS. 

4.  Multiply  5280  by  &.  Ans.  316f. 

5.  Multiply  329  by  5J.  Ans.  1809^. 
Suggestion.  —  Multiply  by  \,  and  then  by  5,  adding  results. 

6.  Multiply  435  by  16|.  Ans.  7250. 
Note.  —  By    changing    the   whole  number    to    a   fraction 

(12  =-j-)}  the  above  ten  examples  may  be  solved  as  in  the 
following  article. 

ART.  35.   To  multiply  one  fraction  by  another. 

Ex.  1.  Multiply  f  by  }. 

*X*=T^  =  H  Ans' 

Explanation.  —  Since  £  is  \  of  3,  f  times  f  must  equal  J  of 
3  times  J.     3  times  f-  is  -y-,  and  1  of  y-  is  f  |. 
Ex.  2.  Multiply  f  by  f  of  }|. 

2 

$      2     ~t£      4      , 
-X.-  of  —  =—  Ans. 
il      $        lo      15 


RTJIL,  K. 

Multiply  the  numerators  together,  and  also  the  denomina- 
tors. Or, 

Indicate  the  multiplication  to  be  performed,  and  cancel  the 
factors  common  to  the  numerators  and  denominators. 

Note.  —  It  is  not  necessary  first  to  reduce  compound  frac- 
tions to  simple  ones. 

Examples. 

2.  Multiply  |  by  |. 

3.  Multiply  -f7¥  by  2T-  4-ns-  I- 

4.  Multiply  f  by  J. 

5.  Multiply  56  by  J.  Ans.  49. 

6.  Multiply  T<V  by  24.  Ans.  13f 

7.  Multiply  81  by  7|.  -4»w.  65|. 

8.  Multiply  111  by  9f. 

9.  Multiply  |  of  |f  by  T8o  of  f  f  >4rcs.  T«¥. 

10.  Multiply  f  of  T\  by  T9T—  |. 

11.  Multiply  |  of  8  by  9  times  f  . 


COMMON     FRACTIONS.  47 

12.  Multiply  8^—61  by  9|-f|.  Ans.  19f. 

13.  Multiply  256  by  12^.  Ans.  3152. 

14.  Multiply  12i  by  16|.  Ans.  208. 


DIVISION    OF    COMMON    FRACTIONS 

ART.  36.  To  divide  a  fraction  by  a  whole  number. 
Ex.  1.  Divide  TV  by  3. 

fP=T3o  A™.     Or,  Tf-3  =  ^=T\  Ans. 
Explanation.  —  To  divide  a  number  by  3  is  to  take  |  of  it  ; 
i  of  fV=T3o,  or  i  of  T«v=^T=T3r. 


Divide  the  numerator  of  the  fraction  by  the  whole  number, 
or  multiply  its  denominator. 

32  x  a  m.  p  1  e  s'. 

2.  Divide  f  }  by  9. 

3.  Divide  JJ  by  7. 

4.  Divide  6J  by  9.  ^715.  if. 

5.  Divide  6084f  by  5. 

5)6084| 

1216,  4|  unolivided 
4f  =-y-5-5=-i-f     Hence  6084|s-5=:1216i|  Ans. 

6.  Divide  308|  by  12.  Ans.  25}f 

7.  Divide  32006}  by  9.  Ans.  3556^- 

8.  Divide  1000fV  by  5.  Ans.  200  rV 
ART.  37.  To  divide  a  who^e  number  by  a  fraction. 

Ex.  1.  Divide  12  by  f  . 

12  Or,  3)12 

A  4 

3)48  _4 

16  Ans.  16  ^W5. 

Explanation.  —  Since  1  is  contained  in  12  twelve  times,  |  is 
contained  in  12  four  times  12  times,  or  48  times,  and  £,  one 


48  COMMON     FRACTIONS. 

third  of  48  times,  or  16  times.     Or,  3  is  contained  in  12  four 
times,  and  f  ,  or  1  of  3,  four  times  4  times,  or  16  times. 

RTJ3L.E. 

Multiply  the  whole  number  by  the  denominator  of  the  frac- 
tion, and  divide  the  product  by  the  numerator.  Or, 

Divide  the  whole  number  by  the  numerator,  and  multiply 
the  result  by  the  denominator. 

Examples. 

2.  Divide  16  by  f  . 

3.  Divide  256  by  if  Ans.  336. 

4.  Divide  225  by  12J. 

5.  Divide  30864  by  1.     By  -}.  Ans.  to  last,  46296. 

6.  Divide  50  by  6f     By  3i. 

7.  Divide  284  by  f  of  f  .  Ans.  1136. 
Note.  —  By  reducing  the   whole  number  to  an  improper 

fraction  the  above  15  examples  may  be  solved  as  in  the  follow- 
ing article. 

ART.  38.  To  divide  one  fraction  by  another. 

Ex.  1.  Divide  &  by  f  . 


Explanation.  —  -Since  £  is  equal  to  \  of  3,  the  quotient  of 
sV,  divided  by  3,  or  /¥,  will  be  four  times  too  small,  and 
hence  the  quotient  of  ^\,  divided  by  1  of  3,  or  f  ,  is  equal  to 
4  times  /„,  or  |f  ==|.  Observe  that  this  is,  in  effect,  the  same 
as  multiplying  the  dividend  by  the  divisor  inverted. 


Invert  the  divisor  and  proceed  as  in  multiplication  of 
fractions. 

Examples. 

2.  Divide  f  by  \. 

3.  Divide  f  by  f.  Ans.  If 

4.  Divide  7i  by  8^. 

5.  Divide  4|  by  6|.  Ans.  ||. 

6.  Divide  18|  by  15}. 


DIVISION     OF     COMMON     FRACTIONS.  49 

7.  Divide  f  of  J  by  J  of  5f.  Ana.  T2T. 

8.  Divide  J  of  4j  by  1  of  5£. 

9.  Divide  J  of  8  by  f  of  7.  Ana. 

10.  Divide  12  J  of  J  by  8J  of  J. 

11.  Divide  A  +  4}  by  4}—  3}i. 

12.  Divide  TV  of  44  —  1  of  T7T  by  5\—  4}. 

13.  Divide  125f-62}  by  37*. 

14.  Divide  4i  +  6f  by  T5T. 

15.  Divide  9TV+4j  x  f  by  6|.  u4w*.  Iff 
ART.  39.  To  reduce  a  complex  fraction  to  a  simple  one. 

Ex.  Keduce  I  to  a  simple  fraction. 


Explanation.  —  It  is  evident  that  a  complex  fraction  is  only 
an  indicated  division  of  one  fraction  by  another,  in  which  the 
numerator  is  the  dividend,  and  the  denominator  the  divisor. 
In  the  example  J  is  the  dividend,  and  |  the  divisor.  "We  may 
proceed  as  in  division,  or  it  is  plain  that  the  same  result  may 
be  obtained  by  multiplying  the  extremes,  4  and  9,  for  a  nume- 
rator, and  the  means,  5  and  8,  for  a  denominator. 

RTJ3L.E, 

Divide  the  numerator  of  the  complex  fraction  by  the,  de- 
nominator as  in  division  of  fractions. 

E  x  a  m  pies. 

2.  Eeduce  -  to  a  simple  fraction. 

T72 

2_ 

3.  Eeduce  -  to  a  simple  fraction.  Ans.  |. 


4.  Keduce  - — *—  to  a  simple  fraction. 

33i 

5.  Keduce  -^r~  to  a  simple  fraction.  Ans.  |. 

**» 


50  MISCELLANEOUS     PROBLEMS. 

6.  Keduce  -|  to  a  simple  fraction. 

4" 

7.  Keduce  I  to  a  simple  fraction.  Ans. 


8.  Keduce  r~^~i  to  a  simple  fraction.  Ans. 

~  ~ 


MISCELLANEOUS     PROBLEMS. 

ART.  40,  1.  What  is  the  sum  of  f ,  £,  f ,  and  T72  ? 

2.  What  is  the  difference  between  }  and  f  ? 

3.  Multiply  |  by  3£. 

4.  Divide  f  by  3j. 

5.  What  is  the  sum,  difference,  product,  and  quotient  of 
3J  and  2i  ? 

6.  What  will  be  the  cost  of  15^  pounds  of  butter  at  16| 
cents  a  pound  ?  Ans.  $2.58i. 

7.  At  $4|  per  yard,  how  many  yards  may  be  bought  for 
$11$  ?  .^s.  2f 

8.  At  28$  cents  per  bushel,  how  many  bushels  of  oats  may 
be  bought  for  16 1  cents  ?  •  Ans.  ^  bushels. 

9.  How  many  pounds  in  four  bags,  the  first  containing 
360} ,  the  second  580},  the  third  296|,  and  the  fourth  375 T\  ? 

Ans.  1614jf  Ibs. 

10.  In  5  hogsheads  of  sugar  containing,  respectively,  945^ 
1054^,  963$,  901f f,  and  899f ,  how  many  pounds  ? 

11.  A  man  has  4  lots  ;  the  first  containing  320}|  acres, 
the  second  225f ,  the  third  160|,  and  the  fourth  278f  ;  how 
many  acres  in  all  ?  Ans.  986 ^  A. 

12.  A  man  owes  the  following  sums  :  to  A  $32.56},  to  B 
$44.95T\,  to  C  $32.72},  to  D  $53.31  A,  to  E  192.05TV     How 
much  does  he  owe  in  all  ? 

13.  A  farm  is  divided  into  5  fields,  containing,  respectively, 
as  follows  :  20|,  56T9T,  36f ,  9|,  and  102jf  acres.     How  many 
in  all  ?  Ans.  226f  f  f  A. 

14.  A  man  purchased  }  of  a  yard  of  velvet  at  the  rate  of 
$3.62^  per  yard  ;  what  did  it  cost  him  ?          Ans.  $3.17T36 . 


MISCELLANEOUS     PROBLEMS.  51 

15.  A  man  owned  f  of  a  boat,  and  sold  i  of  f  of  his  share 
for  $2400.     At  that  rate,  what  was  the  whole  worth  of  it  ? 

Ans.  $19200. 

16.  James  has  f  of  an  orange.     He  gives  Horace  ^  of  this 
amount,  and  then  divides  the  remainder  equally  between  three 
boys.     What  part  does  each  of  the  three  boys  receive  ? 

Ans.  }. 

17.  If  f  of  a  barrel  of  flour  costs  $5,  how  much  will  2  bags 
of  flour  cost,  one  containing  |  of  a  barrel,  and  the  other  f  of  a 
barrel?  Ans.  $12. 

18.  Bought  |  of  f  of  5  j  yards  of  broadcloth  at  the  rate  of 
§3.50  per  yard.     Required  the  cost  of  it.         Ans.  $8.02-^. 

19.  What  will  be  the  cost  of  7£  yards  of  muslin  at  12i 
cents  per  yard,  and  12 1  yards  of  gingham  at  18  f  cents  per 
yard?  ,  Ans.  $3.28}. 

20.  I  purchased  7  loads  of  coal,  each  containing  15  f  bushels, 
at  12^  cents  per  bushel.     Required  the  cost.      Ans.  $13.78j. 

21.  A  owns  f  of  a  vessel,  and  sells  f  of  his  share  to  B  for 
$45000.     What  part  of  the  vessel  has  he  left,  and  what  is  it 
worth  at  that  rate  ?  Ans.  ^  left,  worth  $15,000. 

22.  A  owns  f  .of  a  ship.     He  sells  |  of  his  share  to  B  for  a 
certain  sum,  and  |  of  what  he  then  owns  to  C  for  $5,000. 
What  was  the  value  of  the  whole  ship  at  C-'s  rate  of  purchase  ? 

Ans.  $72000. 

23.  A  owns  T%  of  an  acre  of  land,  and  B  f  of  an  acre. 
How  much  does  A  own  more  than  B  ?      How  many  times 
more  ?     How  much  do  they  both  own  ? 

Ans.  to  the  last,  |f. 

24.  I  have  $1000  and  wish  to  lay  out  $346f  of  it  in  sugar 
at  8^  cents  per  pound,  and  the  remainder  in  coffee  at  11  f  cents 
per  pound.     How  many  pounds  of  coffee  do  I  buy  ? 

Ans.  5561-fVa  Ibs. 

25.  A  merchant  directed  his  agent  to  lay  out  f  of  $2354  in 
wheat  at  87|  cents^per  bushel ;  T30-  of  it  in  rye  at  56  £  cents  per 
bushel ;  and  the  remainder  in  oats  at  31  £  cents  per  bushel 
How  many  bushels  of  each  did  he  purchase  ? 

Ans.  to  last,  564f  f  bus.  of  oats. 


52  DECIMAL     FRACTIONS. 

26.  What  will  8.J-  pounds  of  sugar  cost  at  18f  cents  per 
pound  ? 

27.  A  has  6|  acres  in  one  lot  and  7|  in  another  ;  B  has  5f 
times  as  much  as  A.     How  many  has  he  ?       Ans.  83f  ]•  A. 

28.  What  will  f  of  f  yards  of  cloth  cost  at  f  of  f  dollars 
per  yard  ? 

29.  A  merchant  owns  f  of  a  mercantile  establishment  worth 
$64,000.     He  sells  f  of  his  share  to  B,  and  |  the  remainder  to 
C.     How  much  does  he  receive  from  B  and  C  respectively, 
and  what  part  has  he  remaining  ?      Ans.  From  B,  $33600. 

From  C,  $11200. 
Has  left,  TV 

30.  A  merchant  has  33T7F  yards  of  cloth,  from  which  he 
wishes  to  cut  an  equal  number  of  coats,  pants,  and  vests. 
What  number  of  each  can  he  cut  if  they  contain  3f ,  2|,  and 
1  j  yards  respectively  ?  Ans.  4. 

31.  A  merchant  owns  T97  of  a  stock  of  goods;  -f  of  the  whole 
stock  were  destroyed  by  fire,  and  -^  of  the  remainder  damaged 
by  water.     "What  part  of  the  whole  stock  remained  uninjured  ? 
How  much  did   the  merchant  lose,  provided   the  uninjured 

are  sold  at  cost  for  $5400,  and  the  damaged  at  half  cost? 

An$.  -£•$  uninjured. 
Merchant  Loses,  33,918.75. 


DECIMAL    FRACTIONS. 

ART.  41,  A  decimal  fraction  is  a  fraction  whose  denomi- 
nator is  some  power  of  ten,  thus  T5¥,  Tf  ¥?  T/O  are  decimal  frac- 
tions. 

In  writing  a  decimal  fraction  the  denominator  is  omitted, 
the  numerator  being  written  in  such  a  manner  as  to  indicate 
the  denominator.  This  is  done  by  continuing  the  decimal 
scale  used  in  writing  whole  numbers  below  or  to  the  right  of 
the  order  of  units. 

The  first  order  at  the  right  of  units  is  tenths,  the  second 
hundredths,  the  third  thousandths,  etc. 


DECIMAL     FRACTIONS.  53 

A  point  ( . ),  called  the  decimal  point  or  separatrix,  is 
placed  between  the  order  of  units  and  the  order  of  tenths.  The 
orders  at  the  left  of  the  decimal  point  express  a  whole  number; 
the  orders  at  the  right  a  decimal  fraction,  or  simply  a  decimal. 

The  names  of  the  orders  at  the  right  and  left  of  the  decimal 
point,  and  the  relation  of  decimals  to  whole  numbers,  are  shown 
in  the  following 


TABLE. 


3  j  S  § 

3  C  «  2  O 

I  J  j  1  4    I  I  4    j 

4        7       £  I  jl  -3-7,         c  o  "S        3 

1  1  I  I  I  ,1  I  I  I 

i   a   J  e  «  I   &  3  s   s  ;g  s  «   s 

3333333  333333 


WHOLE  NUMBER.  DECIMALS. 

The  orders  at  the  right  of  the  decimal  point  are  called 
decimal  places.  Thus  in  .0223  there  are  four  decimal  places. 

The  denominator  of  a  decimal  fraction  is  1  with  as  many 
ciphers  annexed  as  there  are  decimal  places  in  the  numerator. 
Thus  the  denominator  of  .00035  is  100000. 

Since  the  value  of  decimal  orders  decreases  in  a  tenfold  ratio 
from  left  to  right,  every  cipher  placed  between  decimal  figures 
and  the  decimal  point,  thus  removing  them  one  place  to  the 
right,  diminishes  their  value  tenfold.  Thus  .025  is  one-tenth 
of  .25. 

Ciphers  placed  at  the  right  of  decimal  figures  do  not  change 
their  value.  Thus  .250=.25  and  .8700=.87. 

A  whole  number  and  a  decimal  written  together  constitute 
a  mixed  number,  or  a  mixed  decimal,  as  25.037. 

Note. — When  the  denominator  of  a  decimal  fraction  is 
written,  it  is  usually  considered  a  common  fraction  ;  the  term 
decimal  being  only  applied  when  the  denominator  is  under- 
stood. The  above  definition  of  a  decimal  fraction  is,  however, 
strictly  correct. 


54  NUMERATION     OF     DECIMALS. 


NUMERATION    OF    DECIMALS. 

ART.  42.  In  reading  a  decimal  expressed  in  figures,  two 
things  are  necessary  :  1st.  To  ascertain  what  the  figures  ex- 
press as  a  whole  number.  2d.  To  ascertain  the  order  of  the 
right  hand  figure.  In  a  whole  number,  the  right  hand  figure 
is  always  units.  In  a  decimal,  it  is  found  by  commencing  at 
the  decimal  point  and  naming  each  order  toward  the  right. 

Ex.  1.  Express  in  words  .002015607. 

Explanation.  —  Commence  at  the  right  hand  and  separate 
the  figures  into  periods  as  in  whole  numbers,  thus  :  2.015.607. 
Next  commence  at  the  decimal  point  and  name  the  orders  to 
the  last  decimal  figure,  which  is  billionths.  Then  read  the 
decimal  as  a  whole  number,  adding  the  name  of  the  last  deci- 
mal figure,  thus  :  two  millions,  fifteen  thousand,  six  hundred 
and  seven  billionths.  Hence  the  following  general 


Read  the  figures  as  in  whole  numbers  and  add  the  name  of 
the  last  decimal  order. 

DE  x  a  m  pies. 

Express  in  words  the  following  decimals  : 

2.  .01012305 

3.  .000027 

4.  .500006 

5.  207.0084 

Suggestion.  —  Read  the  whole  number  as  units,  and  then 
the  decimal. 

6.  7080.00607008 

7.  .002005505 

8.  .006 

9.  600.06 

10.  1000.001 

11.  25000000.000250 
-12.  206.000000206 


NOTATION     OF     DECIMALS.  55 


NOTATION    OF    DECIMALS. 

ART.  43.  Ex.  1.  Express  in  figures  ten  thousand  five  hun- 
dred and  five  milliontKs. 

Explanation.  —  Write  the  numerator  of  the  decimal  as  a 
whole  number,  thus  :  10505.  Then  place  the  decimal  point  so 
that  the  right  hand  figure  may  be  millionths,  filling  up  the 
vacant  order  with  a  cipher,  thus  :  .010505. 


Write  the  decimal  as  a  whole  number,  and  place  the  decimal 
point  so  that  the  right  hand  figure  shall  be  of  the  same  name 
as  the  decimal. 

Examples. 

Express  in  figures  : 

1.  Twenty-five  thousandths. 

2.  Twenty-five  millionths. 

3.  Twenty-five  hundredths. 

4.  Two  hundred  and  five  ten-thousandths. 

5.  Two  hundred  and  five  ten-millionths. 

6.  Twenty  thousand  and  five  millionths. 

7.  Two  thousand  and  four  ten-thousandths. 

8.  Six  hundred  and  fifty  units  and  thirty-seven  thou- 
sandths. 

9.  One  unit  and  one  millionth. 

10.  Five  thousand  units  and  five  thousandths. 

11.  Two  thousand  five  hundred  and  six  hundredths.. 
Note.  —  The  above  is  an  improper  decimal.  •  The  point  falls 

between  the  figures,  thus  :  25.06. 

12.  Nine  millions,  fifteen  thousand,  and  twenty-five  mil- 
liontlis. 

13.  Eight  thousand  and  forty  ten  millionths. 

14.  One  million  and  one  millionths. 


56  REDUCTION     OF     DECIMALS. 


REDUCTION    OF    DECIMALS. 

ART.  44.  A  whole  number  may  be  changed  to  a  mixed 
decimal,  or  a  decimal  to  an  equivalent  decimal  of  a  lower  order 
by  annexing  ciphers.  Thus  :  .025=  .025000,  and  325.  =  325.000. 
This  is,  in  effect,  multiplying  both  terms  of  a  fraction  by  the 
same  number. 

A  mixed  decimal  may  be  reduced  to  an  improper  decimal 
fraction  by  removing  the  decimal  point  and  writing  the  de- 
nominator, thus  :  205.025=a-f  l-jrl^.  The  following  examples 


will  make  the  student  familiar  with  these  changes  : 

1.  Keduce  .205  to  millionths.  Ans.  .205000. 

2.  Eeduce  .0225  to  ten-millionths. 

3.  Eeduce  .14  to  hundred-thousandths. 

4.  Keduce  .0205  to  billionths. 

5.  Keduce  .02301  to  billionths. 

6.  Keduce  .5  to  millionths. 

7.  Keduce  25.  to  thousandths.  Ans.  25.000. 

8.  Keduce  404.  to  hundredths. 

9.  Keduce  4.  to  millionths. 

10.  Keduce  40.  to  ten-thousandths. 

11.  Keduce  62.5  to  thousandths.  Ans.  62.500. 

12.  Keduce  6.02  to  millionths. 

13.  Keduce  4.506  to  billionths. 

14.  How  many  tenths  in  40  units  ?  Ans.  400. 

15.  How  many  millionths  in  5  thousandths  ?     Ans.  500. 

16.  How  many  thousandths  in  62.304  ?         Ans.  62304. 

17.  How  many  millionths  in  36.0394  ?     Ans.  36030400. 

18.  How  many  hundredths  in  400  ?  Ans.  40000. 

19.  How  many  tenths  in  6  tens  ? 

20.  How  many  millionths  in  one  million  ? 

ART.  45.  To  reduce  a  decimal  to  an  equivalent  common 
fraction. 

Ex.  Keduce  .25  to  an  equivalent  common  fraction. 

=  T-  Ans. 


REDUCTION     OF     DECIMALS.  57 


Supply  the  denominator,  and  reduce  the  fraction  to  its 
lowest  terms. 

E  x  am  pies. 

Eeduce  the  following  decimals  to  equivalent  common  frac- 
tions : 

1.  .20506.  7.  62.25.            Ans.  62J. 

2.  .250.  Ans.  J.          8.  6.225. 

3.  .75.  9.  80.025.        Ans.  80¥V- 

4.  .125.  Ans.  1.        10.  8.0375. 

5.  .0075.  11.  15.02.          Ans.  l^\. 

6.  .0125.  Ans.  TV         12.  120.0125. 

ART.  46.  To  reduce  common  fractions  to  an  equivalent 
decimal. 

Ex.  Keduce  £  to  a  decimal. 

4)3.00 

.75  Ans. 

Explanation.—  -}=J  of  3  ;  but  3=3.00,  hence  }  =iof  3.00 
=.75. 

33,  TILE. 

Annex  ciphers  to  the  numerator  and  divide  by  the  denomi- 
nator. Point  off  as  many  decimal  places  as  there  are  annexed 
ciphers. 

IE  x  a  m.  p  1  e  s  • 

2.  Keduce  £  to  a  decimal. 

3.  Keduce  Y7T  to  a  decimal. 

4.  Keduce  Tf  T  to  a  decimal.  Ans.  .024. 

5.  Keduce  ¥~  to  a  decimal. 

6.  Keduce  2570-  to  a  decimal. 

7.  Keduce  12  f  to  a  mixed  decimal.  Ans.  12.75. 

8.  Keduce  25T3¥  to  a  mixed  decimal. 

9.  Keduce  300T|¥  to  a  mixed  decimal. 

10.  Keduce  ^-f-8-  to  a  mixed  decimal. 

11.  Keduce  6.37£  to  a  mixed  decimal.  Ans.  6.3775. 

12.  Keduce  .07|  to  a  pure  decimal.  Ans.  .07125. 


58  ADDITION     OF     DECIMALS. 


ADDITION    OF    DECIMALS 

ART.  47.  Ex.  1.  Add  6.025,  65.37,  100.0035,  and  .875. 

6.025 
65.37  Explanation.  —  Since  decimals  are  written 

100.0035  upon  the  same  scale  as  whole  numbers,  they 

******  are  added  in  the  same  manner. 

172.2735  Ans. 


Write  the  numbers  so  that  the  figures  of  the  same  order 
shall  stand  in  the  same  column. 

Add  as  in  whole  numbers,  and  point  off  in  the  result  as 
many  decimal  places  as  are  equal  the  greatest  number  found  in 
any  of  the  numbers  added. 

Note.  —  The  decimal  points  of  the  several  decimals  added 
and  of  the  answer  stand  in  the  same  column. 

rf  Examples. 

Ex.  2.  Add  .37J,  .02561,  .00015,  .5J,  .27i,  and  .026. 
.37|     =  .3775 
.02561=  .02565 
.00015=  .00015 
.5i       =  .533331 
.271     =  .273331 
.026     =  .026 

1.23596|  Ans. 

3.  What  is  the  sum  of  256  thousandths,  3005  millionths, 
207  ten-thousandths,  45  hundred-thousandths,  7  hundredths, 
and  20037  millionths  ? 

4.  Add  .00675,  4.5689,  3.00007,  2.05,  3.6800|,  .9375,  8.75, 
6.4375. 

5.  What  is  the  sum  of  307  millionths,  56  1  ten-thousandths, 
68f  hundredths,  5  hundred-thousandths,  256i  tenths,  18f  ten- 
millionths,  and  25  hundredths  ?  Ans.  26.568483875. 

6.  Add  375  ten-thousandths,  375  thousandths,  375  hun- 
dredths, 375  tenths,  and  375  units.  Ans.  416.6625. 

7.  A  man  bought  4  barrels  of  molasses,  each  containing 


SUBTRACTION     OF     DECIMALS.  59 

respectively  30.37|,  31 J,  33.6756,  and  28.6 1  gallons.      How 
many  gallons  in  all  ? 

8.  A  man  bought  5  lots,  containing,  respectively,  26.62^, 
220.2007,  56.9£,  5.8T\,  and  150.68J  acres.     How  many  acres 
in  all  ?  Ans.  460.31945. 

9.  Add  360.00025,  3.75,  567.893,  60,000.637,  200.050006, 
.0003625,  20.05. 

10.  Find  the  sum  of  2|,  .625,  6TV,  3.6TJT,  26.3125,  5.6, 


SUBTRACTION    OF    DECIMALS. 

ART.  48.  Ex.  1.  From  60.025  take  3.0825. 
60.0250 

3.0825  Explanation. — Same  as  in  addition. 

56.9425  Ans. 

RTJIL.E. 

Write  the  numbers  as  in  addition  of  decimals,  subtract  as 
in  wJiole  numbers,  and  point  off  as  in  addition  of  decimals. 

Examples. 

2.  From  .37^  take  .0187}. 

.37i     =.375000 
.0187| =.018775 

.356225  Ans. 

3.  From  4.05  take  2.00075. 

4.  From  8.1  take  5.37f . 

5.  From  362  ten-thousandths  take  1056  millionths. 

Ans.  .035144 

6.  From  875  thousandths  take  62  ten-millionths. 

7.  From  100.001  J  take  93.00075.  Ans.  7.00105. 

8.  A  man  bought  8.75 T3FV  yards  of  linen  at  one  time  and 
29.0056  at  another.      He  afterwards  sold  25 ff  yards.     How 
many  has  he  left  ? 

9.  From  7  tenths  take  7  ten-millionths. 
10.  From  10001  ten-thousandths  take  10001  ten-millionths. 


60  DIVISION     OF     DECIMALS. 


MULTIPLICATION    OF    DECIMALS. 

ART.  49.  Ex.  1.  Multiply  2.5  by  .25. 

2.5  Explanation.  —  2.5==  H,  -25=TVo;  an(i  hence 

2.5  x  .25=  if  x  TV*=  rWir=.625. 


.625 

RULE. 

Multiply  as  in  whole  numbers,  and  point  off  as  many  figures 
in  the  product  as  there  are  decimal  places  in  the  multiplicand 
and  multiplier. 

Note.  —  If  there  are  not  enough  figures  in  the  product,  prefix 
ciphers.  Thus:  1.6  x.  016=.0256  ;  .01  x.  003  =.00003. 

IE  x  a  m.  pies. 

2.  Multiply  37.5  by  4.5. 

3.  Multiply  $16.37^  by  3  hundredths. 

4.  What  is  12  hundredths  of  $100.15  ? 

5.  What  is  7  tenths  of  .201  thousandths  ? 

6.  Multiply  .0015  by  .125. 


DIVISION    OF    DECIMALS. 

ART.  50.  All  the  examples  in  Division  of  Decimals  fall 
under  one  of  three  cases,  viz.  : 

1.  When  the  decimal  places  in  the  dividend  equal  those  of 
the  divisor. 

2.  When  the  decimal  places  of  the  dividend  exceed  those  of 
the  divisor. 

3.  When  the  decimal  places  of  the  dividend  are  less  than 
those  of  the  divisor. 

These  three  cases  are  illustrated  in  the  following  examples  : 
Ex.  1.  Divide  6.25  by  .25. 

2  Explanation. — Since  the  quotient  arising 

J* '  '_  - — .  from  dividing  one  number  by  another  of  the 

same  denomination  is  a  whole  number,  625 
hundredths  divided  by  25  hundredths  must  give  25  units. 


DIVISION     OF     DECIMALS.  61 

Ex.  2.  Divide  .864  by  3.6. 

Explanation. — 36  tenths  (3.6)  is  con- 

3.6).864.(.24  Ans.       tained  in  8  tenths  (the  same  denomina- 
-YTT  tion)  0  times  ;  hence  there  are  no  units 

144  in  the  quotient.     36  tenths  is  contained 

in  86  hundredths  2  tenths  of  a  time  and 
14  hundredths  remaining.     36  tenths  is  contained  in  144  thou- 
sandths 4  hundredths  of  a  time.     Hence  .864-^-3. 6 =.24. 
Ex.  3.  Divide  13.2  by  .033. 

Explanation.— 132  =  13.200  =  13200  thou- 
.033)13.200       sandths,  which  divided  by  33  thousandths  must 
400.      give  400,  a  whole  number. 

33,  TILE. 

FIRST  CASE. — Divide  as  in  whole  numbers  ;  the  quotient 
will  be  in  units. 

SECOND  CASE. — Divide  as  in  whole  numbers,  and  point  out 
as  many  places  in  the  quotient  as  the  decimal  places  of  the 
dividend  exceed  those  of  the  divisor. 

THIRD  CASE. — Make  the  decimal  places  of  the  dividend 
equal  to  those  of  the  divisor  by  annexing  ciphers,  and  then  pro- 
ceed as  in  whole  numbers.  The  quotient  will  be  in  units. 

Note. — In  either  case,  if  there  is  a  remainder,  the  division 
may  be  continued  by  annexing  ciphers  ;  but  each  cipher  thus 
annexed  will  give  one  decimal  figure  in  the  quotient. 

Proof. — It  is  well  for  the  student  to  test  the  correctness  of 
his  answer  by  multiplying  the  divisor  by  the  quotient.  If  the 
quotient  is  correct,  the  product  will  be  the  dividend. 

E  x  a  TOO.  pies. 

4.  Divide  6.25  by  2.5.  Ans.  2.5. 

5.  Divide  6.25  by  .025.  Ans.  250. 

6.  Divide  .625  by  25. 

7.  Divide  25.6  by  .016. 

8.  Divide'256  by  .16. 

9.  Divide  .256  by  160.  Ans.  .0016. 

10.  Divide  .001  by  100. 

11.  Divide  .0025  by  50. 


62  CONTRACTIONS. 

12.  Divide  4.2  by  31i. 

13.  Divide  $16  by  $0.25. 

14.  Divide  3  by  1.25.  Ana.  .024. 
Note. — In  this  example,  we  annex  two  ciphers  to  make  the 

division  possible  ;  this  gives  two  decimal  places  in  the  dividend. 
We  add  another  cipher  to  obtain  the  quotient  figure  4  ;  thus 
making  in  all  three  decimal  places. 

15.  Divide  5  by  400. 

16.  Divide  9  by  1500. 

17.  Divide  6.4  by  80. 

18.  Divide  .1  by  .121.  .  Ans.  .08. 

19.  Divide  6|  by  .08. 

20.  Divide  16|  by  .033i. 


CONTRACTIONS. 

ART.  51.  To  divide  a  decimal  by  10,  100,  1000,  etc.,  re- 
move the  decimal  point  as  many  places  to  the  left  as  there  are 
ciphers  in  the  divisor. 

Note. — If  there  are  not  figures  enough  in  the  number,  prefix 
ciphers. 

IE  x  am.  pies. 

1.  Divide  6.25  by  100.  Ans.  .0625. 

2.  Divide  .25  by  10. 

3.  Divide  .45  by  1000. 

4.  Divide  .01  by  100. 

ART.  52.  To  multiply  a  decimal  by  10,  100,  1000,  etc.,  re- 
move the  decimal  point  as  many  places  to  the  right  as  there 
are  ciphers  in  the  multiplier.  Thus  :  62.5  x  100  =  6250  ; 
4.3  x  10=43. 

$43.50 
150. 
1.68 


Multiply 


456.30 
1000. 
38. 
5.60 


by  100. 


REDUCTION     OF     DENOMINATE    NUMBERS.       63 


REDUCTION    OP    DENOMINATE 
NUMBERS. 

ART.  53.  A  denominate  number  is  composed  of  concrete 
units  of  different  weights,  measures,  etc. 

Denominate  numbers  are  of  two  kinds,  simple  and  com- 
pound. 

A  simple  denominate  number  is  composed  of  units  of  a 
single  denomination,  as  10  pounds  ;  12  hours. 

A  compound  denominate  number,  or  simply  a  compound 
number,  is  composed  of  units  of  several  denominations  of  the 
same  weight,  measure,  etc.,  as  5  days  16  hours  20  minutes. 

Reduction  is  the  process  of  changing  the  form  of  a  denom- 
jnate  number  without  altering  its  value. 

Remark. — In  treating  of  Denominate  Numbers,  we  omit 
both  tables  and  rules.  The  student  is  supposed  to  be  familiar 
with  the  tables  in  common  use. 

ART.  54.  To  reduce  a  denominate  number  of  a  higher  de- 
nomination to  a  simple  denominate  number  of  a  lower. 

Examples. 

1.  Kecluce  5  Ib.  6  oz.  10  pwt.  18  gr.  of  silver  to  grains. 

lb.     oz.     dwt.      er. 

5    6     10    18  Ans.  31938  gr. 

12 

66     oz. 
20 

1330  pwt. 

24 
31938  gr. 

2.  How  many  seconds  in  10  hours  ? 

10      h.  Ans.  36000  s. 

60 

600    m. 
60 


36000  s. 


64       REDUCTION     OF     DENOMINATE     NUMBERS.    . 

3.  Keduce  J  Ib.  of  butter  to  drams.  Ans.  199£  dr. 

ix16=ii5.;xl6=:-L-V--=199i  dr. 

4.  Keduce  g-J¥  yd.  to  inches.  Ans.  f  £  in. 

aVo  x  3  =  sVo,  x  12=f  f.  Ans.     Or,  JLy^jj  =  .3  in. 

5.  Keduce  .48  yd.  to  nails.  Ans.  7.68  na. 

.48  yd. 


L92  qr. 

4 
~7j68na. 

6.  Reduce  12i  bu.  to  pints.  Ans.  800  pt. 

7.  In  f-  of  an  acre  how  many  perches  ?         Ans.  140  p. 

8.  Keduce  12  h.  20  m.  to  seconds.  Ans.  44400  s^ 

9.  Keduce  £  hhd.  of  wine  to  pints.  Ans.  378  pt. 

10.  Keduce  .375  T.  to  pounds  (Avoirdupois). 

Ans.  750  Ib. 

11.  In  .7  of  a  bushel  how  many  pints  ?        Ans.  44.8  pt. 
IS.  In  8.75  yd.  how  many  nails  ?  Ans.  140  na. 

13.  Keduce  2|  days  to  minutes.  Ans.  3840  m. 

14.  Keduce  5f  cords  to  solid  feet.  Ans.  736  s.  ft. 

15.  In  .45  of  a  rod  how  many  inches  ?         Ans.  89.1  in. 

16.  Keduce  12  cubic  feet  to  cubic  inches. 

Ans.  20736  c.  in. 

17.  Keduce  13.5  hhd.  of  beer  to  quarts.       Ans.  2916  qt. 

18.  Keduce  5  Ib.  6  oz.  12  pwt.  of  gold  to  pwt. 

Ans.  1332  pwt. 

19.  Reduce  5.24  Ib.  of  calomel  to  ounces.     Ans.  83.84  oz. 

20.  Keduce  7  Ib.  (Troy  weight)  to  grains. 

Ans.  40320  gr. 

21.  Reduce  .65  of  a  yard  to  quarters.  Ans.  2.6  qr. 

22.  In  .24  of  a  ream  of  paper  how  many  sheets  ? 

Ans.  115.2  sheets. 

23.  In  f  of  a  barrel  of  flour  how  many  pounds  ? 

Ans.  78f  Ib. 

24.  Reduce  7  Ib.  8|  oz.  of  butter  to  drams. 

Ans.  1930|  dr 


REDUCTION  OF  DENOMINATE  NUMBERS.   65 

25.  In  j %-$  Ib.  of  brass  how  many  ounces  ?     Ans.  TV2j  oz. 
ART.  55.   To  reduce  a  simple  denominate  number  of  a  lower 
denomination  to  a  denominate  number  of  a  higher. 

Examples. 

1.  Reduce  15969  gr.  to  pounds. 

Ans.  2  Ib.  9  oz.  5  pwt.  9  gr. 
24)15969  gr. 
20)665    pwt.     9gr. 
12)33_   oz.     5  pwt, 
~2~"   Ib.     9oz. 

2.  Reduce  f  of  an  inch  to  the  fraction  of  a  yard. 

in.  ft.  yd. 

¥xrV— rls"?  Xj=sjjy.  Ans.  ^|¥  yd. 

Explanation. — J  of  an  inch  is  J  of  TV  of  a  ft.,  which  is 
ft.,  and  T£¥  of  a  foot  is  Tlj  of  1  of  a  yard=¥JT  yd. 

3.  Reduce  .48  of  a  nail  to  the  decimal  of  a  yard. 

4).48  n.  Ans.  .03yd. 

4)12  qr. 
.03  yd. 

4.  Reduce  25.6  dr.  to  the  decimal  of  a  pound. 

16)25.6  dr.  Ans.  .1  Ib. 

16)1.6  oz. 
.lib. 

5.  Reduce  414  gal.  wine  to  hhd.         Ans.  6  hhd.  36  gal. 

6.  Reduce  2461  pwt.  to  pounds. 

Ans.  10  Ib.  3  oz.  1  pwt. 

7.  Reduce  1357  pts.  to  bushels.   Ans.  21  bu.  6  qts.  1  pt. 

8.  Reduce  98  furlongs  to  miles.  Ans.  12  m.  2  fur. 

9.  Reduce  307200  perches  to  square  miles.    Ans.  3  sq.  m. 

10.  Reduce  4032  gills  to  hhd.  of  wine.  Ans.  2  hhd. 

11.  Reduce  T3F  gal.  to  the  fraction  of  a  hhd.      Ans.  -^^j. 

12.  Reduce  T7T  hours  to  the  fraction  of  a  day.     Ans.  ^f -5. 

13.  Reduce  6|  pt.  to  the  fraction  of  a  bu.  Ans.  T\. 

14.  Reduce  645  in.  to  yd.  Ans.  17  yds.  2  ft.  9  in. 

15.  Reduce  2176  en.  ft,  to  cords.  Ans.  17  cords. 

16.  Reduce  1152f  qt.  to  hhd.  Ans.  4  hhd.  36.2  qt. 

17.  Reduce  523  nails  to  yards.       Ans.  38  yd.  3  qr.  3  na. 


66       REDUCTION     OF     DENOMINATE     NUMBERS. 

18.  Reduce  23.04  drams  to  Ibs.  Ans.  .09  Ib. 

19.  Reduce  184.8  hours  to  weeks.  Ans.  1.1  weeks. 

20.  How  many  acres  in  a  street  5  rods  wide  and  2i  miles 
long  ?  Ans.  25  acres. 

ART.  56.  To  find  what  part  one  denominate  number  is  of 
another  ? 

Note.  —  The  first  ten  examples  contain  abstract  numbers,  and 
are  designed  to  introduce  denominate  numbers. 

3S  x  a  m.  pies. 

1.  8  is  what  part  of  12  ?  Ans.  1. 
Explanation.  —  1  is  ^  °f  12,  and  8  is  8  times  TV  of  12, 

which  is  T\  of  12=  f  of  12. 

2.  9  is  what  decimal  part  of  15  ?  Ans.  .6. 
Explanation.  —  9  is  T9j  of  15,  and  T9?  changed  to  a  decimal 

is  .6. 

3.  |  is  what  part  of  £  ?  Ans.  f  . 

|=f.     Or,f=TVand}=T'T;  TV=-TV=i    Since  TV  is  i  of  A, 
T33  is  8  times  1  of  T9¥=f  of  T\. 

4.  What  part  of  GI  is  2|  ?  ^4rcs.  if. 
23      i 

_  !L  __  2_  _  1  6  Or     92  -  8  _  16    o-nrl    £  1  -  1   3  -  3  9    •      16-     39  -  1  6 

j.—  •  J_3  —  3T-  Jr?    ^3-—  3—-  8~   an(1   b2—  "2~—  F-   ?     -8-~"^~—  38^' 


5.  15  is  what  part  of  12  ?  Ans  f  . 

6.  27  is  what  part  of  48  ?  ^4rcs.  T\  . 

7.  What  decimal  part  of  72  is  54  ?  Ans.  .75. 

8.  What  decimal  part  of  f  is  f  ?  ^4rcs.  .8. 

9.  What  decimal  part  of  10  is  4£  ?  Ans.  .45. 

10.  What  part  of  .45  is  .09  ?  Ans.  }. 

11.  2  ft.  6  in.  is  what  part  of  a  yard  ?  ^4rcs.  f  . 
2  ft.  6  in.=30  in.,  and  1  yd.=36  in.  ;  30  in.-f-36  in.=f. 
Suggestion.  —  Reduce  denominate  numbers  to  the  same  de- 

nomination. 

12.  What  part  of  a  week  is  5  d.  10  h.  ?  Ans.  f  f  . 

13.  What  part  of  2  acres  is  3  R.  25  p.  ?  Ans.  f  }. 

14.  What  decimal  part  of  5  hours  is  40  minutes  ? 

Ans.  .13i. 


DENOMINATE     NUMBERS.  67 

15.  What  decimal  part  of  5  gals,  is  3  qts.  1  pt.  ? 

Ans.  .175. 

16.  What  part  of  $5  is  87  J  cents  ?  Ans.  T\. 

17.  What  decimal  part  of  a  gallon  is  3  pints  ? 

Ans.  .375. 

18.  What  part  of  .45  Ib.  Troy  is  .45  oz.  ?  Ans.  TV 

19.  £  oz.  is  what  part  of  f  Ib.  Avoirdupois  ?     ^TIS.  T|T. 

20.  4  quires  of  paper  is  what  decimal  part  of  a  ream  ? 

Ans.  .2. 

21.  What  part  of  a  mile  is  6  fur.  16  rds.  ?  Ans.  f . 

22.  What  decimal  part  of  a  pound  is  10  oz.  4  pwts.  ? 

Ans.  .85. 

23.  What  decimal  part  of  a  bushel  is  3  pks.  4  qts.  ? 

Ans.  .875. 

24  What  part  of  a  week  is  3  d.  17  h.  36  m.  ?     Ans.  T«T. 
ART.  57.  To  reduce  a  fraction  of  a  higher  denomination  to 
integers  of  a  lower. 

Examples. 

1.  Reduce  £  of  a  day  to  integers.  Ans.  14  h.  24  m. 

d.  b.  h.         b.  m. 

3X24 72 "IAS       2X60 f)A 

J  ~~5~ -"-^S?     5  ^r*' 

2.  Reduce  .85  of  a  day  to  integers.         Ans.  20  h.  24  m. 

.85  d. 
24 
20.40  h. 

60 
2~400m. 

3.  Reduce  .375  hhd.  to  integers. 

Ans.  23  gals.  2  qts.  1  pt. 

4.  Reduce  .9  Ibs.  Troy  to  integers.    Ans.  10  oz.  16  pwts.  . 

5.  Reduce  £  rod  to  integers.  Ans.  4  yds.  1  ft.  9  in. 

6.  Reduce  .5625  cwt.  to  integers. 

Ans.  2  qrs.  6  Ibs.  4  oz. 

7.  Reduce  30  T\  hhds.  to  integers. 

Ans.  30  hhds.  27  gals.  2  qts.  2  gills. 

8.  Reduce  f  mile  to  integers. 

Ans.  4  fur.  17  rds,  4  yds.  10  in. 


68  DENOMINATE     NUMBERS. 

9.  Eeduce  250.35  Ibs.  Troy  to  integers. 

Ans.  250  Ibs.  4  oz.  4  pwts. 

10.  Keduce  .8  mile  to  integers.  Ans.  6  fur.  16  rods. 

11.  Keduce  £f  to  integers.  Ans.  13s.  4d. 

12.  Keduce  .45  peck  to  integers.          Ans.  3  qts.  1.2  pts. 

13.  What  is  the  value  of  f  week  ? 

Ans.  2  d.  19  h.  12  m. 

14.  What  is  the  value  of  .75  bu.  ?  Ans.  3  pecks. 

15.  What  is  the  value  of  T\  day  ?          Ans.  13  h.  30  m. 


ADDITION   OF   DENOMINATE   NUMBERS. 

ART.  58.  Ex.  1.  Add  together  5  Ibs.  6  oz.  13  pwts.  22  grs.  ; 

12  Ibs.  9  oz.  18  pwts. ;  7  oz.  19  pwts.  21  grs. ;  24  Ibs.  11  oz. 

18  grs. 

ibs.    oz.    pwts.    grs.  Explanation.— Having     written 

5       6     13     22  numbers  of  the  same  denomination  in 

12       9     18     00  the  same  column,  add,  reducing  as 

7     19     21  • 

far  as  possible  the  lower  denomina- 
^4     11     UU     lo 

^o — Ti — To — To~  A  tions  to  a  higher.      In  this  example. 

4o     11     1^     lo  Ans.  . 

the  sum  of  the  grains  is  61  grs.= 

2  pwts.  13  grs.     Write  13  grs.,  and  add  the  2,  pwts.  to  the 
column  of  pwts.,  and  proceed  as  before. 

2.  A  man  purchased  4  loads  of  corn  :  the  first  contained 
25  bu.  3  pks.  7  qts.  1  pt.  ;  the  second,  30  bu.  2  qts. ;  the  third, 
37  bu.  1  pk  ;  the  fourth,  29  bu.  1  pk,  7  qts.  1  pt.     How  much 
did  he  buy  ?  Ans.  122  bu.  3  pks.  1  qt. 

3.  Find  the  sum  of  5  gals.  3  qts.  1  pt.  ;   10  gals.  1  pt.  1 
gill ;  25  gals.  1  pt.  ;  19  gals.  1  qt.  1  gill ;  and  30  gals.  1  pt.  3 
gills.  Ans.  90  gals.  2  qts.  1  pt.  1  gill. 

4.  A  man  has  4  farms.     The  first  contains  110  A.  3  K.  25 
P. ;  the  second,  95  A.  1  K.  20  P.  ;  the  third,  205  A.  0  R. 
15  P. ;  and  the  fourth,  90  A.  3  K.  35  P.     How  many  acres  in 
all  ?  Ans.  502  A.  1  K.  15  P. 


DENOMINATE     NUMBERS.  69 

5.  I  purchase  of  a  merchant  19  yds.  3  qrs.  of  cloth  ;  of  a 
second,  25  yds.  3  qrs.  2  na. ;  of  a  third,  17  yds.  3  na.  How 
many  yards  did  I  buy  ?  Ans.  62  yds.  3  qrs.  1  na. 


SUBTRACTION   OF   DENOMINATE   NUMBERS. 

ART.  59.  Ex.  1.  From  12  Ibs.  6  oz.  take  7  Ibs.  9  oz.  13  pwts. 
22  grs. 

11  17        19          24  Minuend  changed  in  form. 

Ibs.  oz.  pwt.  grs. 

12  6    00    00  Minuend. 

7    9     13    22  Subtrahend. 
4862  Remainder. 

Ex.  2.  From  3  m.  7  fur,  30  rds.  take  5  fur.  38  rds.  10  ft. 
9  in. 

36        69        15*      12  Minuend  changed  in  form. 

m.  fur.  rds.  ft.   in. 

3    7    30  00    0 

5    38  10    9 

3     1    31  5i  3 


3     1     31       59  Ans. 

3.  From  1  m.  take  4  fur.  3  rds,  4  yds.  2  ft.  6  in. 

4.  From  2  T.  4  cwt.  take  17  cwt.  2  qrs.  8  Ibs. 

5.  How  long  from  June  12,  1855,  to  April  3,  1859  ? 

mo.       da. 

1859    4      3 
1855    6     12 

3    9    21  Ans. 

6.  How  long  from  the  signing  of  the  Declaration  of  Inde- 
pendence, July  4,  1776,  to  the  battle  of  New  Orleans,  January 
8,  1815  ?  Ans.  38  yrs.  6  mo.  4  da. 

7.  From  the  battle  of  Lexington,  April  18,  1775,  to  the 
battle  of  Montebello,  May  5,  1859  ?         Ans.  84  yrs.  17  da. 

8.  How  long  from  the  battle  of  Saratoga,  Sept.  7,  1777,  to 
Perry's  victory,  Sept.  19,  1813  ?  Ans.  36  yrs.  12  da. 


70  DENOMINATE     NUMBERS. 


MULTIPLICATION  OF  DENOMINATE  NUMBERS. 
ART.  60.  Ex.  1.  Multiply  5  fur.  35  rds.  16  ft.  9  in.  by  5. 

m.     fur.      rds.       ft.        in. 


5 

35 

16     9 
5 

3 

5 

20 

*    9 
1=6 

3    5    20      13    Ans. 

2.  What  is  the  distance  round  a  square  field,  each  side  of 
which  is  35  rds.  5  yds.  2  ft.  9  in.  in  length  ? 

Ans.  3  fur.  24  rds.  1  yd.  2  ft. 

3.  What  is  the  weight  of  5  watch  chains,  each  containing 
1  oz.  7  pwts.  13  grs.  of  gold  ?        Ans.  6  oz.  17  pwts.  17  grs. 

4.  Bought  7  loads  of  corn,  each  containing  29  bu.  3  pks. 
7  qts.  1  pt.  ;  how  much  corn  did  I  buy  ? 

Ans.  209  bu.  3  pks.  4  qts.  1  pt. 

5.  Bought  11  pieces  of  broadcloth,  each  containing  34  yds. 
1  qr.  3  na.  ;  how  many  yards  did  1  buy  ? 

Ans.  378  yds.  3  qrs.  1  na. 

6.  How  much  wine  in  7  casks,  each  containing  75  gals. 
3  qts.  1  pt.  ?  Ans.  531  gals.  0  qts.  1  pt. 


DIVISION  OF  DENOMINATE  NUMBERS. 

ART.  61.  Ex.  1.  Divide  1  m.  3  fur.  28  rds.  5  yds.  2  ft.  8  in. 
by  5. 

m.        fur.      rds.       yds.        ft.        In. 

5)1 3_28 5__2 8_ 

2     13   ~4~    1      5J. 

2.  A  man  divided  1578  acres  of  land  equally  between  7 
children  ;  what  was  the  share  of  each  ? 

Ans.  225  A.  1  R.  28^  P, 


DENOMINATE     NUMBERS.  71 

3.  A  piece  of  cloth  containing  36  yds.  3  qrs.  will  make 
5  suits  of  clothes  ;  how  much  cloth  in  each  suit  ? 

Ans,  7  yds.  1  qr.  If  na. 

4.  Seven  men  purchased  8  cwt.  3  qrs.  20  Ibs.  of  sugar. 
What  was  the  share  of  each  ?    Ans.  1  cwt.  1  qr.  2  Ibs.  13-f  oz. 

5.  Four  men  agreed  to  share  equally  3  sacks  of  coffee,  each 
containing  2  cwt.  1  qr.  15  Ibs.     What  was  the  share  of  each  ? 

Ans.  1  cwt.  3  qrs.  5  Ibs. 


MISCELLANEOUS    PROBLEMS. 

ART.  62.  Ex.  1.  What  will  .65  of  a  ream  of  paper  cost  at 
20  cents  a  quire  ?  Ans.  $2.60. 

2.  What  will  f  of  a  ream  of  paper  cost  at  £  of  a  cent  per 
sheet?  Ans.  $2.25. 

3.  What  will  f  of  a  barrel  of  beef  cost  at  6^  cents  a  pound  ? 

Ans.  $4.69. 

4.  What  mustjbe  the  height  of  a  wood-bed  that  is  12  feet 
long  and  3^  feet  wide  to  hold  just  one  cord  ?      Ans.  3^T  ft. 

5.  What  will  it  cost  to  excavate  a  cellar  18|  feet  long,  15| 
feet  wide,  and  9  feet  deep,  at  20  cents  per  cubic  yard  ? 

Ans.  $19.12. 

6.  How  many  cords  of  wood  in  a  pile  40  feet  long,  7|  feet 
high,  and  4  feet  wide  ?  Ans.  9|  cords. 

7.  What  will  .75  of  a  hhd.  of  wine  cost  at  75  cents  a  pint  ? 

Ans.  $283.50. 

8.  Bought  12  barrels  of  flour  at  $6.50  per  barrel,  and  sold 
the  same  at  retail  at  4  cents  a  pound.     How  much  did  I  gain  ? 

Ans.  $16.08. 

9.  The  cabin  of  the  steamer  Bostona  is  165  feet  long  and 
18  feet  wide.     What  will  it  cost  to  carpet  the  same  with 
Brussels  carpeting  f  of  a  yard  wide  at  80  cents  a  yard  ? 

Ans.  $704. 

10.  At  25  cents  a  sq.  yd.,  what  will  it  cost  to  plaster  the 
ceiling  of  a  room  18|  feet  long  and  16  feet  wide  ? 

Ans.  $8.22. 


72  DENOMINATE     NUMBERS. 

11.  At  20  cents  a  sq.  yd.,  what  will  it  cost  to  plaster  both 
sides  of  a  partition  wall  52  feet  long  and  13 1  feet  high,  and  an- 
other wall  149  feet  long  and  11  feet  high  ?        Ans.  $52.02. 

12.  A  gentleman's  garden  200  feet  long  and  180  feet  wide 
is  enclosed  by  a  tight  board  fence  5£  feet  high  ?     What  will  it 
cost  to  paint  the  fence  at  10  cts.  per  sq.  yd.  ?     Ans.  $46.44. 

13.  How  many  bricks,  each  being  8  in.  long  and  4  in.  wide, 
will  it  take  to  surround  the  above  garden  with  a  walk  6  feet 
in  width  ?     What  will  be  the  cost  of  the  bricks  at  $4  per  1000  ? 

Ans.  21168  bricks  ;  $84.67  cost. 

14.  A  miller  ground  5000  bushels  of  wheat,  taking  from 
each  bushel  4  quarts  of  wheat  as  toll.     How  many  bushels  of 
wheat  does  he  grind  for  his  customers,  and  what  does  he  re- 
ceive for  the  work,  wheat  being  worth  87^  cents  a  bushel  ? 

Ans.  4375  bushels,  $546.87*. 

15.  What  will  be  the  cost  of  25  boards,  each  being  15  ft. 
long  and  10  in.  wide,  at  $30  per  thousand  ?      Ans.  $9.37^. 

16.  What  cost  9  cwt.  1  qr.  18  Ibs.  12  oz.  at  $6.40  per  cwt.  ? 

Ans.  $60.40. 

17.  What  will  10  Ibs.  8  oz.  8  pwts.  of  gold  cost  at  $300  per 
pound?  Ans.  $3210. 

18.  What  will  3  f  hhds.  of  molasses  cost  at  10  cents  per 
quart?  Ans.  $94.50. 

19.  What  will  be  the  cost  of  papering  the  walls  of  a  room 
40  feet  long,  30  feet  wide,  and  9  feet  high,  at  30  cents  a 
bolt,  each  bolt  being  9  yards  long  and  18  inches  wide  ? 

Ans.  $9.33i. 

20.  A  farmer  sold  30  bu.  2  pks.  1  qt.  If  pts.  of  clover  seed 
at  $3.60  per  bushel.     How  much  did  he  receive  ? 

Ans.  $191.10. 

21.  How  many  bushels  of  coal  will  a  boat  100  feet  long, 
42  feet  wide,  and  4  feet  deep  contain,  a  bushel  of  coal  being  1^ 
of  a  cubic  foot  ?  Ans.  10800. 

22.  If  there  are  6  yds.  3  qrs.  2  na.  in  one  suit  of  clothes, 
how  many  yards  will  clothe  an  army  of  128,000  men  ? 

Ans.  880,000. 


PRACTICE. 


73 


PRACTICE. 

ART.  63,  Many  of  the  examples  met  with  in  common 
business,  may  be  easily  solved  by  exercising  a  little  tact,  espe- 
cially where  the  prices  used  contain  an  aliquot  part  of  a  dollar, 
or  where  the  cost  of  compound  quantities  is  required. 

A  few  examples  will  illustrate  this  method. 

The  aliquot  parts  of  a  dollar  in  common  use  are  shown  in 


the  following 


50  cts.=  i  of  $1.00 


TABLE 

I 


25  cts.  =4  of  50    cts. 
12i  «  =  |  of  25     " 

6i  "  =  4.  of  12i   " 
16|  "  =1  of  33i   " 

81  "  =|of!6f   " 


16|  " 

61    " 


=  i  of  50 


25  "  =  i  of  $1.00 
12  .V  "  =  i  of  $1.00 

6}  "  =TV  of  81.00 
33}  "  =  i  of  $1.00 
16|  "  =  i  of  81 00 

8}  "  =  TVof  $1.00 

Ex.  1.  Required  the  cost  of  24  yds.  of  muslin  at  12i  cts. 
a  yd. 

Solution.— At  $1.00  a  yd.  it  is  worth  $24.00. 

At  12.i  cts.  a  yd.  it  is  worth  only  i  of  $24.00,  which  is 
$3.00.  Ans. 

Ex.  2.  Find  the  cost  of  56  yds.  at  37  J  cts.  a  yd. 

Solution.— At  $1.00  a  yd.  the  cost=$56.00. 

At  25  cts.  a  yd.  the  cost=i  of  $56.00= $14.00. 

At  12i  cts.  a  yd.  the  cost=i  of  $14.00=$7.00. 

The  sum  of  the  last  two  results =$21.00.  Ans. 

Ex.  3.  Required  the  cost  of  56  bbls.  of  flour  at  $6.87^  a  bbl. 
50  cts.=  i  $56.00=the  cost  at  $1.00  a  bbl. 


25      "  = 


$385.00       =  "     "     "  $6.87, 
Note. — See  table  of  aliquot  parts. 


1 

Ii 

a  bbl. 

a 

$336.00 

28.00 
14.00 
7.00 

=the  cost  at  $6.00 

it  tt  it  KC\ 

=  "  «  «  .25 

74 


PRACTICE. 


Ex.  4.  Kequired  the  cost  of  75  gals,  of  wine  at  $< 

50    cts.=    i      $75.00=the  cost  at  $1.00  a  gal. 

3.93f 

$225.00     =the  cost  at  $3.00    a  gal. 
37.50     =  "     "     "       .50       " 
18.75     =  "     "     "      .25       " 


f  a  gal. 


25      "  = 


= 


9.375  = 

4.6875= 


.121 
.06} 


$3.93£ 


Ex. 


$295.3125=  < 
5.  Find  the  cost  of  25  bu.  at  ^.o.^- 


"1  ft  2    r»j-a    
J.UTT   OLo.  

Ex.6. 
25    cts.= 

6i    "  = 

Re 
i 

4 

i 

1 

2 

$25.00  =the  cost  at  $1.00    a  bu. 
4.16|=  u     "     "      .16|      " 

a  yard. 

$29.166=  "     "     "  $1.16}      " 
quired  the  cost  of  75  yds.  at  43  £  cts. 
$75.00     =the  cost  at  $1.00  a  yd. 

18.75     =  "      "     "       .25    a  yd. 
9.375  =  "     "     "      .12i     « 
4.6874=  "     "     "      .06}     " 

Ex. 

50    cts 
61    " 


$32.8125=  <       "     "      .43  J     " 
7.  Kequired  the  cost  of  45  bu.  at  56}  cts.  a  bu. 
_$45.00_  =the  cost  at  $1.00    a  bu. 
~22.50~  =  "     "     "       .50      " 
2.8125=  "     "     "      .06}    " 
~ 


Ex. 
25  cts. 

Ex. 

2qrs.= 


8.  Find  the  cost  of  9762  bu.  at  25  cts.  a  bu. 
I  i  |  $9762.     =the  cost  at  $1.00  a  bu. 

$2440.50=  "     "~~«      25      "~ 

9.  Kequired  the  cost  of  7  yds.  3  qrs.  at  75  cts.  a  yd. 
i 


$0.75     =the 
7 

cost  of  1  yd. 

"     "  7  yds. 
"     "              2  qrs. 
"     "'              1  qr. 

$5.25     =  " 
.375  =  " 
.1875=  " 

Ex. 
a  bu. 

cts, 


$5.8125=   '  i  7  yds.  3  qrs. 

10.  Kequired  the  cost  of  256  bu.  of  corn  at  18f  cts. 


$256.00=the  cost  at  $1.00    a  bu. 


6} 


32.00=  " 
16.00=  " 

$48.00="^ 


.06}     " 


PRAC  TICE. 


75 


Ex.  11.  Find  the  cost  of  15  Ibs.  15  oz.  of  butter  at  25  cts.  a  Ib. 


8  oz.= 

4  "  = 
2  "  = 
1  "  = 

Ex. 

cts.  a  Ib 
4  oz.= 

2  "  = 
1  "  = 

Ex.: 

at  $9.50 
2  qrs.= 

1    " 

5  lbs.= 

5   "   = 

Ex.  ] 

68  f  cts. 
2  qts.= 

1    " 

Ipt.  = 

Ex.  1 

61  cts.= 

i 

2 

1 
i 
1 

12. 

1 

4 

I 

1 
I 

L3. 
a 

i 
j 

i 

5 
1 

0 

4. 

as 

1 

j 

I 

5. 

T 

$0.25        =  the  cost  of  lib. 
15 

3.75        =     "     "     "  15  Ibs. 
125       =     "     «     "                8oz. 
625     =     "     "     "                4  " 
3125  —     u     "     "                2  " 
15625=     "     "     "                1  " 

$3.984375=     "      "     "  15  Ibs.  15  oz. 
Required  tne  cost  of  9  Ibs.  7  oz.  of  cheese  at  12i 

$0.125         =the  cost  of  1  Ib. 
9 

1.125        =  "    '  "     "9  Ibs. 
3125     =  "     "     "            4oz. 
15625  =  "     "     "            2  " 
78125=  "     "     "            1  " 

$1.1796875=  "     "    "  9  Ibs.  7  oz. 
Required  the  cost  of  5  cwt.  3  qrs.  10  Ibs.  of  sugar 
cwt. 

$9.50  =the  cost  of  1  cwt. 
5 

$47.50  =  "     "     "  5  cwt. 
4.75  =  "      "     "             2  qrs. 
2.375=  "     "     "             1   " 
475=  "     "     "                       5  Ibs. 
475=  "     "     "                      5   " 

$55.575=  "      "     "  5  cwt.  3  qrs.  10  Ibs. 
Find  the  cost  of  15  gals.  3  qts.  1  pt.  of  molasses  at 
al 
$0.6875       =the  cost  of  1  gal. 
15 

1.03125       =  "     "     "  15  gals. 
34375     =  "      "     "               2  qts. 
171875  =  "     "     "               1   " 
859875=  "     "     "                         Ipt. 

$10.9141125 
Required  the  cost  of  875  bu.  at  $1.06j  a  bu. 
V    $875.00=  the  cost  at  $1.00    a  bu. 
54.69=  "     "     "      .06i     " 

$929.69= 


$1.06i 


76  PRACTICE. 

Ex.  16.  If  a  man  walk  24  m.  7  fur.  25  rds.  in  one  day ; 
how  far  can  he  walk  in  5  d.  11  h.  50  m.  ? 

Ans.  137  m.  0  fur.  23T5¥\  rds. 

Remark. — This  example  may  be  solved  in  the  same  manner 
as  the  preceding  ;  the  only  difference  is,  the  multiplicand  (24 
m.  7  fur.  25  rds.)  is  a  compound  number. 

Ex.  17.  What  will  be  the  cost  of  3  qrs.  2  na.  at  $4.50  a  yd.  ? 

Ans.  $3.94. 

Ex.  18.  Kequired  the  cost  of  13  cwt.  3  qrs.  20  Ibs.  of  cheese 
at  $9.12i  a  cwt.  Ans.  $127.29. 

Ex.  19.  Find  the  cost  of  a  ham,  weighing  15  Ibs.  13  oz.  at 
13  cts.  a  Ib.  Ans.  $2.06. 

Ex.  20.  What  will  be  the  cost  of  17  A.  1  K.  15  P.  of  land 
at  $25.25  per  acre  ?  Ans.  $437.93. 

Ex.  21.  Find  the  cost  of  19  yds.  at  $4.37i  a  yd. 

Ex.  22.  What  are  156  bu.  3  pks.  7  qts.  1  pt.  of  wheat  worth 
at  93J  cts.  a  bu.  ?  Ans.  $147.17. 

Ex.  23.  Find  the  cost  of  87i  yds.  at  87i  cts.  a  yd. 

Ans.  $76.56. 

Ex.  24.  If  a  man  walk  27  m.  5  fur.  15  rds.  in  one  day ; 
how  far  can  he  walk  in  15  d.  10  h.  45  m.  ? 

Ans.  439  m.  1  fur.  26  rds. 

Ex.  25.  If  a  man  earn  6  Ib.  15  oz.  15  dr.  of  cheese  in  one 
day  ;  how  much  can  he  earn  in  7  d.  7  h.  ? 

Ans.  51  Ibs.  5  oz.  6{  dr. 

Ex.  26.  A  man  can  plow  2  A.  1  B.  25  P.  in  a  day  ?  how 
much  can  he  plow  in  5£  days  ?  Ans.  12  A.  3  K.  13 £  P. 

Ex.  27.  Find  the  cost  of  6  T.  5  cwt.  3  qrs.  20  Ibs.  of  hay  at 
$16.62^-  a  T.  Ans.  $104.57. 

Ex.  28.  Kequired  the  cost  of  10  loads  of  coal,  each  contain- 
ing 15^  bu.  at  12i  cts.  a  bu.  Ans.  $19.37i. 

Ex.  29.  What  will  be  the  cost  of  making  29  m.  7  fur.  35 
rds.  of  road  at  $975.75  a  mile  ?  Ans.  $29257.25. 

Ex.  30.  Kequired  the  cost  of  10  cords  75  ft.  of  wood  at 
$2.87  i-  a  cord.  Ans.  $30.43. 

Ex.  31.  Kequired  the  cost  of  55  bbls.  of  flour  at  $6.68|  a 
bbl.  Ans.  $367.81i. 


RATIO.  77 


RATIO. 

ART.  64.  Ratio  is  the  relation  of  one  number  to  another  of 
the  same  kind,  and  is  expressed  by  their  quotient.  Thus  the 
ratio  of  8  to  12  is  expressed  by  12-^-8,  or  -1/-  ;  and  the  ratio  of 
5  to  3  by  3-^5,  or  |. 

A  ratio  is  commonly  expressed  by  separating  the  two  num- 
bers by  a  colon.  Thus  the  ratio  of  8  to  12  is  written  8  :  12  ; 
the  ratio  of  5  to  3  is  written  5  :  3. 

The  two  numbers  are  called  terms  of  the  ratio — the  first, 
or  divisor,  being  called  the  antecedent,  and  the  second,  or  divi- 
dend, the  consequent. 

When  the  antecedent  is  less  than  the  consequent,  the  value 
of  the  ratio  is  greater  than  1,  and  the  ratio  is  called  increas- 
ing ;  when  the  antecedent  is  greater  than  the  consequent,  the 
value  of  the  ratio  is  less  than  1,  and  the  ratio  is  called  de- 
creasing. 

Ratios  are  of  three  kinds  ;  simple,  complex,  and  compound. 

A  simple  ratio  is  the  ratio  of  two  whole  numbers,  as  5  :  6, 
and  12  :  5. 

A  complex  ratio  is  the  ratio  of  two  fractional  numbers,  as 
I  :  |,  2i  :  5i,  and  2.5  :  .5. 

A  compound  ratio  is  the  product  of  two  or  more  simple 
ratios,  as  (5  :  4)  x  (3  :  2)  x  (3  :  4). 

Compound  ratios  may  be  written  in  the  form  of  fractions, 
as  i  x  |  x  f .  In  stating  problems,  the  ratios  are  written  under 

5 

each  other  without  the  sign  of  multiplication,  as  3 

3 

A  compound  ratio  may  be  reduced  to  a  simple  one  by  mul- 
tiplying all  the  antecedents  together  for  a  new  antecedent  and 
all  the  consequents  for  a  new  consequent. 

Note. — The  numbers  that  form  a  ratio  must  be  either  both 
abstract,  or  both  concrete.  When  concrete,  they  must  be  of 
the  same  denomination,  or  such  as  may  be  reduced  to  the  same 


78  RATIO. 

denomination,  otherwise  a  division  is  impossible.     5  men  have 
no  ratio  to  10  hogs,  nor  3  pens  to  6  hens. 

What  is  the  value  of  each  of  the  following  ratios  : 

1.  7  :  14.       Ans.  2.  10.  1.5  :  .45. 

2.  6:3.         Ans.  }.  11.  .25 :  .6. 

3.  15  :  45.  12.  2.5  :  10. 

4.  3:9.  13.  10  :  2.5. 

5.  6:2.  14.  $5  :  $15. 

6.  45  : 15.  15.  $0.75  :  $3. 

7.  f  :  f.  16.  2  ft.  6  in.  :  10  ft. 

8.  2i :  |.  17.  2  Ib.  8  oz.  :  10  oz. 

9.  f  :  T\.  18.  10  oz.  :  2  Ib.  8  oz. 


Ans. 


PROPORTION. 

ART.  65.  A  Proportion  is  an  equality  of  ratios. 

Four  numbers  are  in  proportion  when  the  ratio  of  the  first 
to  the  second  equals  the  ratio  of  the  third  to  the  fourth  ;  thus 
4,  6,  8  and  12  are  in  proportion. 

The  equality  of  two  ratios  may  be  expressed  by  the  sign  of 
equality,  thus  4  :  8=6  : 12  ;  or  by  four  dots,  thus  4  :  8  :  :  6  : 12. 
The  last  mpthod  is  the  more  common,  and  is  read  4  is  to  8  as 
6  is  to  12. 

The  first  ratio  of  a  proportion  is  called  the  first  couplet  ; 
the  second,  the  second  couplet. 

The  first  and  third  terms  of  a  proportion,  being  the  antece- 
dents of  the  two  ratios,  are  called  antecedents  ;  the  second  and 
fourth,  being  consequents  of  the  two  ratios,  are  called  conse- 
quents. 

The  first  and  fourth  terms  of  a  proportion  are  called  ex- 
tremes ;  the  second  and  third  terms,  means. 


RATIO.  79 

Both  ratios  of  a  proportion  must  be  of  the  same  kind,  that 
is,  both  increasing ,  or  both  decreasing,  otherwise  they  cannot 
be  equal.  Hence,  in  every  proportion,  if  the  first  term  is  less 
than  the  second,  the  third  term  is  less  than  the  fourth,  and  if 
the  first  term  is  greater  than  the  second,  the  third  term  is 
greater  than  the  fourth. 

As  ratios  may  be  expressed  in  the  form  of  fractions  (see 
Art.  64),  the  proportion  4  :  8  :  :  6  :  12  may  be  written  £=-V2-. 
By  multiplying  each  of  these  equal  fractions  by  6  (the  denom- 
inator of  the  second),  we  have  1^=12,  and  by  multiplying 
each  of  these  equal  quantities  by  4  (the  denominator  of  the 
first  fraction),  we  have  8x6=12x4.  But  8  and  6  are  the 
means  of  the  above  proportion,  and  12  and  4  its  extremes. 
Hence, 

In  every  proportion,  the  product  of  the  means  equals  the 
product  of  the  extremes. 

Therefore, 

1.  If  the  product  of  the  two  means  of  a  proportion  be 
divided  by  either  extreme,  the  quotient  will  be  the  other  extreme, 

2.  If  the  product  of  the  two  extremes  of  a  proportion  be 
divided  by  either  mean,  the  quotient  loill  be  the  other  mean. 

It  follows  from  the  above,  that  if  any  three  terms  of  a  pro- 
portion are  given,  the  remaining  term  may  be  found.  Find  the 
missing  term  in  each  of  the  following  proportions  : 

1.  15  :  20  :  :  90  :  — . 

2.  —  :  16  :  :  90  :  20. 

3.  45  :  90  :  :  —  :  28. 

4.  27  :  —  :  :  108  : 12. 

5.  i :  f  :  :  |  :  — . 
6.2i:-::|:4. 

7.  i ;  3  .  .  —  .  i^ 

8.  2.5  :  62.5  :  :  15  :  — . 

9.  3.6  :  7.2  :  :  —  :  9.4. 

10.  2i  :  7i  :  :  i  :  — . 

11.  J:  A ::  —  :}. 

12.  i  :*::*:-, 


80  RATIO. 


SIMPLE     PROPORTION. 

ART.  66.  A  Simple  Proportion  is  an  equality  of  two 
simple  ratios. 

The  method  of  finding  the  fourth  term  of  a  simple  proportion, 
the  other  three  being  given,  or  of  solving  problems  by  means 
of  a  simple  proportion,  is  sometimes  called  the  Rule  of  Three. 

In  stating  a  problem  in  simple  proportion,  the  first  and 
second  terms  must  be  of  the  same  denomination  ;  also  the  third 
and  the  answer  sought. 

Ex.  1.  If  5  men  can  do  a  piece  of  work  in  18  days,  how 
many  men  can  do  it  in  10  days  ? 

Explanation.  —  The 


. 
term)  is  to  be  in  men, 

10)90  therefore  5  men  is  the 

~9  men,  4th  term,  or  Ans.       tnird  term-     If  5  men 

can  do  a  piece  of  work 

in  18  days,  it  will  require  more  men  to  do  the  same  work  in  10 
days  (less  time).  Hence  the  second  ratio  is  increasing,  and  the 
first  must  be  increasing,  or  18  days  must  be  made  the  second 
term.  Hence,  10  days  :  18  :  :  5  men  :  Ans.  or  9  men. 

RTJLIE.  , 

Place  the  number  of  the  same  denomination  as  the  answer 
sought  for  the  third  term.  If  the  answer  is  to  be  GREATER  than 
the  third  term,  place  the  greater  of  the  other  tioo  numbers  for 
the  second  term,  and  the  less  for  the  first;  if  the  answer  is  to 
be  less  than  the  third  term,  place  the  LESS  of  the  two  numbers 
for  the  second  term,  and  the  greater  for  the  first. 

Then  divide  the  product  of  the  second  and  third  terms  by 
the  first;  the  quotient  will  be  the  fourth  term,  or  answer. 

Examples. 

2.  If  5  peaches  cost  as  much  as  7  apples,  how  many  apples 
can  you  buy  for  35  peaches  ?  Ans.  49  apples. 


RATIO.  81 

3.  What  will  450  feet  of  lumber  cost  at  $17  per  thousand  ? 

Ans.  $7.65. 

4.  If  150  cows  cost  $1800,  how  many  cows  can  be  bought 
for  $132  ?. 

5.  If  5  men  can  mow  8  acres  of  grass  in  one  day,  how  many- 
men  can  mow  32  acres  in  the  same  time  ?          Ans.  20  men. 

6.  If  a  horse  travels  15  miles  in  1  h.  40  m.,  how  far,  at 
this  rate,  can  it  travel  in  12  hours  ? 

7.  If  a  5  cent  loaf  of  bread  weigh  4  ounces  when  flour  is  $4 
per  barrel,  what  should  be  the  weight  of  a  loaf  when  flour  is 
$7.50  per  barrel  ? 

8.  If  5  yards  of  cloth  cost  $17,  how  many  yards  can  be 
bought  for  $102  ?  Ans.  30  yds. 

9.  A  man  received  $45  for  30  days'  work,  how  much  should 
he  receive  for  25  days'  work  ?  Ans.  $37.50. 

10.  If  12  oz.  of  pepper  cost  20  cents,  what  will  7  Ibs.  of 
pepper  cost  ?  Ans.  $1.86|-. 

11.  A  merchant  failing  can  pay  but  70  cents  on  each  dollar 
of  his  indebtedness.     He  owns  A  $1690,   B  $2000,  and  C 
$1100  :  what  will  each  receive  ?  Ans.  C  $770. 

12.  A  merchant  failing  owes  A  $900,  B  $1200,  C  $1400, 
and  D  $1500.     His  property  is  valued  at  $2800  ;  what  will 
each  creditor  receive  ?  Ans.  D  $840. 


COMPOUND     PROPORTION. 

ART.  67.  A  Compound  Proportion  is  an  equality  of  two 
compound  ratios,  or  of  a  compound  ratio  and  a  simple  one. 

In  solving  problems  in  Compound  Proportion,  sometimes 
called  the  Double  Kule  of  Three,  the  second  ratio  is  always 
simple.  The  first  ratio  may  be  reduced  to  a  simple  ratio  by 
multiplying  ther  antecedents  together  for  a  new  antecedent,  and 
the  consequents  together  for  a  new  consequent.  Hence,  every 

compound  proportion  may  be  reduced  to  a  simple  one. 

6 


82  RATIO. 

The  third  term  of  a  compound  proportion  must  be  of  the 
same  denomination  as  the  answer  sought,  and  each  of  the  simple 
ratios  that  compose  the  compound  ratio  must  be  of  like  de- 
nominations. 

Ex.  1.  If  5  men  can  mow  20  acres  of  grass  in  3  days  by 
working  8  hours  each  day,  how  many  men  will  it  take  to  mow 
80  acres  of  grass  in  4  days,  working  6  hours  each  day  ? 

Ans.  20  men. 

STATEMENT. 

20A.    80A.     )  80*3x8*5 

4  days    3  days    V  :  :  5  men  :  Ans.     Or,  _  ^=20 

6  hours    8  hours  \  20x4x6 

Explanation. — The  answer  required  being  in  men,  place  5 
men  for  the  third  term.  If  it  take  5  men  to  mow  20  acres,  it 
will  require  more  men  to  mow  80  acres  in  the  same  time  ; 
hence,  80  acres  must  be  made  the  second  term  of  the  first 
simple  ratio  of  the  compound  ratio.  If  it  take  5  men  when 
they  work  3  days,  it  will  require  less  men  when  they  work  4 
days  ;  hence,  3  days  is  the  second  term  of  the  second  simple 
ratio.  If  it  take  5  men  when  they  work  8  hours  per  day,  it 
will  require  more  men  when  they  work  but  6  hours  per  day  ; 
hence,  8  hours  is  the  second  term  of  the  third  simple  ratio. 
Reducing  the  compound  ratio  to  a  simple  one,  we  havo 
20  x  4  x  6  :  80  x  3  x  8  :  :  5  :  Ans.}  from  which  we  find  the  fourth 
term  to  be  20. 

By  Cancellation. — Instead  of  stating  a  problem  in  com- 
pound proportion  in  the  above  form,  it  is  more  convenient  to 
arrange  the  third  and  second  terms  in  one  column,  the  first 
terms  in  another  column,  and  cancel  the  factors  common  to  the 
two.  The  correctness  of  the  process  is  evident  from  the  fact, 
that  the  product  of  the  third  and  second  terms  constitutes  a 
dividend,  and  the  product  of  the  first  terms  a  divisor.  The 
quotient  is  the  fourth  term. 

5  44 

,  5  x  $0  x  #  x 


'4 
5  x  4  =  20  Ans. 


RATIO,  83 

RTJ3L.E. 

Place  the  number  of  the  same  denomination  as  the  answer 
sought  for  the  third  term.  Arrange  the  first  and  second  terms 
of  each  of  the  simple  ratios  of  the  compound  ratio  as  in  SIMPLE 
PROPORTION. 

Then,  multiply  the  second  and  tnird  terms  together,  and 
divide  their  product  by  the  product  of  the  first  terms.  The 
quotient  will  be  the  answer.  Or, 

Arrange,  the  third  and  second  terms  in  one  column,  the  first 
terms  in  another  at  the  left  hand,  and  cancel  all  the  factors 
common  to  the  two.  Then,  divide  the  product  of  all  the  un- 
cancelled  factors  of  the  right  hand  column  by  the  product  of  all 
the  uncancelled  factors  in  the  left  hand  column.  The  quotient 
ic  ill  be  the  answer. 

Note. — In  determining  which  number  of  each  ratio  is  to  be 
the  second  term,  reason  from  the  number  in  the  condition. 

Examples. 

2.  If  $900  produce  $50  in  9  months,  what  sum  will  pro- 
duce §450  in  5  months  ?  Ans.  $14580. 

3.  If  it  cost  $25  to  lay  a  sidewalk  10  feet  wide  and  90  feet 
long,  what  will  it  cost  to  make  a  walk  6  feet  wide  and  \  of  a 
mile  long  ? 

4.  If  16  men  can  excavate  a  cellar  90  feet  long,  40  feet  wide, 
and  10  feet  deep  in  15  days  of  8  hours  each,  in  how  many  days 
of  9  hours  each  can  3  men  excavate  a  cellar  60  feet  long,  36 
feet  wide,  and  8  feet  deep  ?  Ans.  34r2y  days. 

5.  If  30  men,  by  working  8  hours  a  day,  can  in  9  days  dig 
a  ditch  40  rods  long,  12  feet  wide,  and  4  feet  deep,  how  many 
men,  by  working  12  hours  a  day  for  12  days,  can  dig  a  ditch 
300  rods  long,  9  feet  wide,  and  6  feet  deep  ? 


PART  SECOND, 


PERCENTAGE. 

ART.  68.  Per  cent,  is  a  contraction  of  the  Latin  phrase  per 
centum,  which  signifies  by  the  hundred. 

Percentage  includes  all  those  operations  in  which  100  is  the 
basis  of  computation. 

The  rate  per  cent,  is  the  number  of  hundredths.  Hence, 
any  per  cent,  of  a  number  is  so  many  hundredths  of  it.  Thus, 

5  per  cent,  of  a  number  is      5    hundredths  of  it. 

30  per  cent,  of  a  number  is    30    hundredths  of  it. 

3i  per  cent,  of  a  number  is      3^  hundredths  of  it. 

\  per  cent,  of  a  number  is        \  hundredths  of  it. 

125  per  cent,  of  a  number  is  125    hundredths  of  it. 

And  so  on. 

Note. — Instead  of  the  words  "  per  cent./'  it  is  now  custom- 
ary to  use  the  character  %  :  thus,  12  per  cent,  is  written  12%  ; 
2J  per  cent.,  2j%. 

ART.  69-  The  rate  per  cent,  may  be  expressed  decimally  by 
writing  it  as  so  many  hundredths.     Thus, 
1    per  cent,  is  written    .01 
7    per  cent,  is  written    .07 
5^  per  cent,  is  written    .05  J- ;  or  .055 
15    per  cent,  is  written    .15 
100    per  cent,  is  written  1.00 

i  per  cent,  is  written    .00^  ;  or  .005 
j  per  cent,  is  written    .OOJ  ;  or  .0025 
2j  per  cent,  is  written    .02^ 
¥V  per  cent,  is  written    .OO^V  ;  °r  .0005 


PERCENTAGE.  85 

Exercises. 

1.  Express  decimally  10  per  cent. 

2.  Express  decimally  12|  per  cent. 

3.  Express  decimally  If  per  cent.  Ans.  .01  £. 

4.  Express  decimally  f  per  cent. 

5.  Express  decimally  T\  per  cent.  Ans.  .001 

6.  Express  decimally  2  per  cent. 

7.  Express  decimally  120  per  cent. 

8.  Express  decimally  250  per  cent. 

9.  Express  decimally  1|  per  cent. 

10.  Express  decimally  f  of  3  per  cent.  Ans.  .015. 

11.  Express  decimally  ^  per  cent. 

12.  Express  decimally  500  per  cent.  Ans.  5.00. 


I. 

ART.  70.  To  find  a  given  per  cent,  of  any  number  or 
quantity. 

Ex.  1.  Sold  a  house  and  lot,  which  cost  me  $1450.75,  at  a 
gain  of  15%.  What  was  the  gain  ? 

Explanation.  —  Since  15%  is  .15,  the  gain  was 
$2T7  6l25       I**  hundredths  of  $1450.75. 

Some  persons  prefer,  and  it  is  sometimes  more  convenient, 
to  find  the  percentage  as  follows  : 

Explanation.  —  1  per  cent,  of  any  number  is 
'     -.  -       .01  of  it  (which  is  found  by  removing  the  decimal 
point  two  places  to  the  left),  and  15  per  cent,  is  15 
times  as  much  as  1  per  cent. 


Multiply  the  given  number  by  the  rate  per  cent.  EXPRESSED 

DECIMALLY.       Or, 

Remove  the  decimal  point  TWO  places  to  the  left,  and  mul- 
tiply by  the  rate  per  cent.  AS  A  WHOLE  NUMBER. 

E  x  a  m  pies. 

2.  What  is  8  per  cent,  of  500  miles  ? 

3.  What  is  6  per  cent,  of  $72.37^  ?  Ans.  $43425. 


86  PERCENTAGE. 

4.  Find  32  per  cent,  of  1200  men. 

5.  Find  25  per  cent,  of  12  hours  30  minutes. 

Ans.  3  h.  7  m.  30  s, 

6.  What  is  1000  per  cent,  of  $1000  ?          Ans.  $10000. 

7.  What  is  |  per  cent,  of  $320  ? 

Note. — The  second  rule  is  most  convenient  in  solving  such 
examples  as  the  above.     Thus,  f  of  $3.20=$1.20. 

8.  What  is  J  per  cent,  of  $15.80  ? 

9.  What  is  li  per  cent,  of  1050  sheep  ?     Ans,  14  sheep. 

10.  Find  2-V  per  cent,  of  134500  bushels.      Ans.  67}  bu. 

11.  33}  per  cent  of  any  number  is  what  part  of  it  ? 

Ans.  £. 

12.  What  is  33i  per  cent,  of  252  cattle  ?     Ans.  84  cattle. 
Note. — When  the  rate  per  cent,  is  a  convenient  part  of  100, 

take  the  same  part  of  the  given  number.     Thus,  33^  per  cent. 
of  252  is  i  of  252 = 84. 

13.  What  is  16|  per  cent,  of  1200  hogs  ?     Ans.  200 hogs. 

14.  Find  66  J  per  cent,  of  660  men.  Ans.  440  men. 

15.  Find  75  per  cent,  (f)  of  4852..  Ans.  3639. 

16.  Find  15  per  cent,  of  25  per  cent,  of  $13.60. 

Ans.  $0.51. 

17.  Find  87^  per  cent.  (|)  of  1632  feet,    Ans.  1428  feet. 

18.  A  merchant  -failing  was  able  to  pay  his  creditors  but  40 
per  cent.     He  owes  A  $3500,  B  $1200,  C  $1134,  D  $650. 
What  will  each  receive  ? 

Ans.  A  $1400,  B  $480,  C  $453.60,  D  $260. 

19.  A  person  at  his  death  leaves  an  estate  worth  $1500  ; 
12  per  cent,  of  which  he  received  from  his  wife  ;  20  per  cent, 
from  speculation  ;  30  per  cent,  from  rise  of  property  ;  25  per 
cent,  from  the  estate  of  an  uncle  ;  and  the  remainder  from  his 
father.     How  much  did  he  receive  from  each  source  ? 

Ans.  to  last,  $195. 

20.  A  has  an  income  of  $1100  per  year  ;  he  pays  10  per 
cent,  of  it  for  board  ;  \  per  cent,  for  washing  ;  2  per  cent,  for 
incidentals  ;  15  per  cent,  for  clothing ;  9  per  cent,  for  other 
expenses.     What  does  each  item  cost,  and  how  much  has  .he 
left  ?  Ans.  He  has  left  $698.50, 


PERCENTAGE.  87 

CASE     II. 

ART.  71.  To  find  what  per  cent,  one  number  is  of  another. 

Ex.  1.  6  is  what  per  cent,  of  25  ? 

/o,  —  -6^o  —  .24.     Ans.  24  per  cent, 

Explanation. — 6  is  •£$  of  25,  which  changed  to  a  decimal 
(Art.  )  equals  24  hundredths  ;  or  24  per  cent. 

Ex.  2.  12  cents  is  what  per  cent,  of  $3  ? 

5V2«  = !-%[ £ £=.04.     u4tts.  4  per  cent. 

Explanation. — Since  only  quantities  of  the  same  denomin- 
ation can  be  compared,  reduce  $3  to  cents,  and  proceed -as 
above. 


Reduce  the  numbers  to  the  same  denomination.  Annex  two 
ciphers  to  the  number  which  is  to  be  the  rate  per  cent.,  and 
divide  the  result  by  the  other  number. 


Examples. 

3.  What  per  cent,  of  $40  is  $12  ?  Ans.  30%. 

4.  What  per  cent,  of  120  yards  is  20  per  cent,  of  90  yards  ? 

5.  2^  dimes  is  what  per  cent,  of  $5  ?  Ans.  f//  .    • 

6.  40  men  is  what  per  cent,  of  150  men  ? 

7.  150  men  is  what  per  cent,  of  40  men  ? 

8.  The  cent  (new  coinage)  contains  22  parts  copper  and  3 
parts  nickle  ;  what  per  cent,  of  it  is  copper  and  what  per  cent, 
nickle  ?  Ans.  Copper  88'/0. 

Nickle  121/,. 
9.  15  per  cent,  is  what  per  cent,  of  60  per  cent.  ? 

Ans.  25°/0. 

10.  A  person  whose  annual  income  is  $450  pays  $125  for 
board,  $140  for  clothing,  $25  for  books,  and  $30  for  sundries  ; 
what  percent,  of  his  income  is  each  item,  and  what  per  cent. 
remains  ?  .        •      Ans.  to  last,  28}%. 

11.  A  morchant  failing  owes  $3500  ;  his  property  is  valued 
at  $'2100.     What  per  cent,  of  his  indebtedness  can  he  pay  ? 

Ans.  60%. 


88  PERCENTAGE. 


S     III. 

ART.  72.  To  find  a  number  when  a  certain  per  cent,  of  it 
is  given. 

Ex.  1.  A  merchant  sells  40  per  cent,  of  his  stock  for  $3500  ; 
what  is  the  value  of  his  whole  stock  at  this  rate  : 

Explanation.  —  Since  $3500  is 

--  x  100=$S750.  Ans.       40  per  cent,  of  his  stock,  1  per 

cent,  is  TV  of  $3500,  or  $87.50, 

and  100  per  cent.,  or  the  whole  stock,  100  times  $87.50,  or  $8750. 
Ex.  2.  A  person  pays  $13.50  a  month  for  board,  which  is 
30  per  cent,  of  his  salary,  what  is  his  salary  ? 

$13.50  $1350 

-brk  -  x  100=  -077-  =$450.  Ans. 
ou  ou 

RTJ3L.E. 

Divide  the  given  number  by  the  given  rate  per  cent,  and 
multiply  the  quotient  by  100.  Or, 

Annex  two  ciphers  to  the  given  number,  and  divide  the 
result  by  the  rate  per  cent. 

Note.  —  When  the  given  number  contains  cents  (see  Ex.  2, 
above),  remove  decimal  point  two  places  to  the  left,  instead  of 
annexing  two  ciphers. 

32  x  a,  m  pies. 

3.  45  is  10  per  cent,  of  what  number  ? 

4.  $3.60  is  15  per  cent,  of  what  number  ? 

5.  $5.62^  is  12^  per  cent,  of  what  number  ?     Ans.  $45. 

6.  Sold  cloth  for  $3.50  per  yard,  which  was  70  per  cent,  of 
its  cost  ;  what  was  the  cost  of  the  cloth  per  yard  ?     Ans.  $5. 

7.  A  boy  spent  60  per  cent,  of  his  money  for  toys,  'and  25 
per  cen't.  for  candies,  and  had  15  cents  remaining  ;  how  many 
cents  had  he  at  first  ?  Ans.  $1.00. 

8.  The  assets  of  a  merchant  are  $45000,  which  is  60  per 
cent,  of  his  indebtedness  ;  what  is  his  indebtedness  ? 

Ans.  $75000. 

9.  The  deaths  in  a  certain  city,  during  the  year,  are  980, 
wjiich  is  3i  per  cent,  of  the  population  ;  what  is  the  number 
of  inhabitants  ?  Ans.  '  28000. 


PEECENTAGE.  89 


ART.  73.  A  number  being  given  which  is  a  given  per  cent. 
more  or  less  than  another  number,  to  find  the  required  number. 
Ex.  1.  Sold  broadcloth  at  $5  per  yard  and  made  25  per 
cent.  ;  what  did  the  cloth  cost  per  yard  ? 
JIQQ  Explanation.  —  Since  I  gain  25  per 

25  cent.,  I  receive  125  cents  for  every  100 

125)500  cents  the  cloth  cost  ;  hence  the  cloth 

4  cost  as  many  tunes  100  cents  as  I  re- 

4  x  100=400  cents.         ceive  times  125  cents,  which  is  4,  and 
Ans.  $4.  4  times  100  cents  is  $4. 

Or  thus  :  Qr  thus  : 

Since  I  gain  25  per  cent.,  the  sum 

-^—  -  received  is  125  per  cent,  of  the  cost; 

|j?      ^  hence,  $5  is   f|f  of  the  cost,  which 

is  found  by  dividing  by  1.25. 

When  the  given  per  cent,  is  a  convenient  part  of  100,  it 
maybe  solved  by  using  the  common  fraction;  thus,  T2-5-=i, 
f  +  A  =  £  ;  hence,  $5  is  f  of  the  cost. 

Ex.  2.  A  drover  lost  12  per  cent,  of  a  flock  of  sheep  by  dis- 
ease, and  then  had  2200  ;  how  many  sheep  in  the  flock  at  first  ? 

Explanation.  —  Since  he  lost  12 
i  c\c\ 
1~~  per  cent,  of  his  sheep,  for  every 

"^^  sheep  at  first  there  remained 
9,  but  88  ;   hence,  the  flock  at  first 

95  x  100=2500  Ans  contained  as  many  times  100  sheep 

Qr  as  there  remained  times  88,  or  25 

0900  x  100  times  100  sheep  =2500  sheep. 

-g-8  --  =2500  Ans.  Or  thus  : 

Since  he  lost  12  per  cent,  of  his 

flock,  there  remained  88  per  cent.  ;  hence,  2200  sheep  must 
be  T8/^  of  his  original  flock,  which  is  2500  sheep. 


Divide  the  given  number  by  100,  inceased  or  diminished 
by  the  rate  per  cent.,  and  multiply  the  quotient  by  100.  Or, 

Divide  the  given  number  by  1,  increased  or  diminished  by 
the  rate  per  cent,  expressed  decimally. 


90  PERCENTAGE. 

Examples. 

3.  168  is  20  per  cent,  more  than  what  number  ?  Ans.  140. 

4.  $63.75  is  15  per  cent,  less  than  what  ?         Ans.  $75. 

5.  The  population  of  a  certain  city  is  25000,  which  is  25 
per  cent,  more  than  it  was  in  1850  ;  what  was  the  population 
in  1850  ?  Ans.  20000. 

6.  A  grocer  sells  flour  as  follows  : 

Extra  Family,  $5.50  per  bbl. 

Superfine,          $4.75    "     " 

Fine,  $4.25    "     " 

and  makes  a  profit  of  12^  per  cent.  ;  what  was  the  cost  of  each 
brand  ?  Ans.  to  last,  $3.77|. 

7.  A  cargo  of  corn  being  injured,  the  owner  was  obliged  to 
sell  the  same  for  $28000,  which  was  at  a  loss  of  30  per  cent.  ; 
what  was  the  cost  of  the  cargo  ?  Ans.  $40000. 

8.  The  sales  of  a  dry  goods  firm  amount  to  $90000  per 
year  ;  f  of  the  sales  were  made  at  a  profit  of  25  per  cent.  ;  T\  at 
a  profit  of  35  per  cent.  ;  and  the  remainder  at  a  profit  of  20 
per  cent. ;  what  was  the  cost  of  goods  ?  Ans.  $71300. 


APPLICATIONS    OF    PERCENTAGE. 

ART.  74.  The  four  preceding  cases  underlie  the  whole  sub- 
feet  of  Percentage  in  all  its  numerous  and  important  applica- 
tions. The  importance  of  fully  understanding  them  can  not 
be  urged  too  strongly  upon  one  who  wishes  to  become  a 
competent  accountant.  It  is  not  enough  to  be  able  to  solve 
the  examples  in  accordance  with  the  directions  of  the  rules. 
Rule  accountants  are  always  liable  to  make  serious  errors.  Do 
I  see-  clearly  why  such  a  process  gives  the  required  result  ? 
To  this  question  the  student  should  be  able  to  give  an  affirma- 
tive answer.  , 

There  is  such  a  thing  as  common  sense,  and  the  use  of  it  in 
solving  practical  business  problems  is  a  sine  qua  non.  The 
answer,  of  almost  any  question  may  be  anticipated,  at  least 
approximately,  previous  to  its  solution.  The  common-sense 


PERCENTAGE.  91 

student  sees  from  the  conditions  of  the  question  about  what 
answer  he  may  expect.  In  solving  a  problem  in  discount,  for 
example,  he  knows  whether  the  present  worth  will  be  nearest 
§3,  $30,  or  $3000.  I  have  often  known  "  rule  students"  to 
hand  in  the  most  ridiculous  answers  to  the  simplest  practical 
problems. 


PROFIT    AND    LOSS. 

ART.  75.  The  price  paid  for  an  article,  or  the  total  expense 
of  producing  it,  is  its  cost  ;  the  amount  received  for  an  article 
by  the  vender  is  its  setting  price.  It  is  evident,  from  this,  that 
the  selling  price  of  the  vender,  or  salesman,  may  be  the  cost  of 
an  article  to  the  purchaser. 

When  an  article  is  sold  for  more  than  its  cost,  there  is  a 
profit,  or  gain  ;  when  it  is  sold  for  less  than  its  cost,  there  is  a 
loss.  The  actual  gain  or  loss  is  the  amount  of  this  increase  or 
decrease. 

Profit  or  loss  is  generally  computed  as  a  given  amount  upon 
every  hundred,  or  at  a  given  rate  per  cent.  The  rate  per  cent, 
is  the  number  of  hundredths  of  the  cost  gained  or  lost. 

Profit  and  Loss,  though  usually,  are  not  always  limited 
to  transactions  in  money.  When  any  quantity,  whether  it 
is- money,  or  goods,  or  tune,  or  distance,  or  any  thing  else, 
undergoes  an  increase  or  decrease,  there  is  gain  or  loss,  and  it 
may  be  computed  at  a  rate  per  cent. 

ART.  76.  All  the  problems  in  Profit  and  Loss  come  under 
one  or  more  of  the  four  following  cases,  which  correspond  to 
the  four  cases  of  Percentage,  already  explained. 

1.  The  cost  and  the  per  cent,  of  gain  or  loss  being  given,  to 
find  the  selling  price. 

KULE. — Multiply  the  cost  by  the  rate  per  cent,  of  gain  or 
loss  expressed  decimally  ;  the  product  ivill  be  the  gain  or  loss. 
The  cost  increased  by  the  gain  or  diminished  by  the  loss  ivill 
be  the  selling  price. 

2.  The  cost  and  the  selling  price  being  given,  to  find  the 
per  cent,  of  gain  or  loss. 


92  PERCENTAGE. 

EULE. — Divide  the  gain  or  loss  ~by  the  COST,  and  express 
the  quotient  decimally. 

3.  The  actual  gain  or  loss,  and  the  per  cent,  of  gain  or  loss 
being  given,  to  find  the  cost. 

KULE. — Divide  the  gain  or  loss  by  the  per  cent,  of  gain  or 
loss,  and  multiply  the  quotient  by  100. 

4.  The  selling  price  and  the  per  cent,  of  gain  or  loss  being 
given,  to  find  the  cost. 

KULE. — Divide  the  selling  price  by  $1  increased  or  dimin- 
ished by  the  rate  per  cent,  expressed  decimally. 

Note. — Keep  in  mind  that  gain  or  loss  is  computed  upon 
the  COST. 

E  x  a  m.  pies. 

1.  For  how  much  per  bbl.  must  I  sell  flour  costing  $4.50  per 
bbl.,  to  gain  16  f  per  cent.  ? 

Explanation. — It  must  be  sold  for  the  cost  plus  16  f  per 
cent,  of  the  cost  (found  according  to  Case  I.,  Percentage)  ;  or, 
since  16|  per  cent.  =  -J-,  it  must  be  sold  for  the  cost  plus  -}  of 
the  cost. 

Remark. — When  the  given  per  cent,  is  a  convenient  part 
of  100,  it  is  best  to  use  the  common  fraction,  Instead  of  the 
given  per  cent. 

2.  A  man  offers  a  farm,  for  which  he  gave  $3450,  for  20 
per  cent,  less  than  its  cost.     What  is  his  price  ? 

Explanation. — He  offers  it  for  the  cost  minus  20  per  cent, 
of  the  cost ;  or,  since  20  per  cent.  —  },  he  offers  it'for  the  cost 
minus  }  of  the  cost,  or  $2760. 

3.  How  must  I  sell  sugars  that  cost  $7,  $8.25,  and  jfclO.50 
per  cwt.  to  gain  12|  per  cent.  ?  Ans.  to  last,  $11. ^lf. 

4.  Bought  linen  cloth  for  45  cents,  50  cents,  and  62^  cents 
per  yard  ;  for  what  per  yard  must  I  sell  it  (being  damaged)  to 
lose  18  per  cent.  ?  Ans.  to  last,  51 }  cts. 

5.  A  merchant  is  selling  cloth  that  cost  $3.75  per  yard  for 
$5  ;  twhat  per  cent,  is  his  profit  ?  Ans.  33;,°fv 

Explanation. — He  gains  $5.00  —  $3.75  =  $1.25  on  each 
yard,  or  on  $3.75,  which  (Case  II.  Percentage)  is  33 £  per  cent. ; 


PERCENTAGE.  93 

or,  since  he  gains  §1.25  on  $3.75,  his  gain  is  -J-f  f  or  1  of  the 
cost,  or  33}  per  cent. 

6.  A  grocer  sells  coffee  that  cost  15  cents  per  Ib.  for  12  cents 
per  Ib.  ;  what  is  his  loss  per  cent.  ?  Ans.  20 yc.  . 

Eemark. — The  simple  question  in  this  problem  is,  what 
per  cent,  of  15  is  3  ? 

f  7.  A  grocer  sells  tea  costing  62 1  cents  per  Ib.  for  75  cents  ; 
sugar  costing  9  cents  for  12^  cents  ;  flour  costing  $5.20  for 
$5.75.  What  does  he  gain  per  cent,  on  each  article  ? 

Ans.  to  last,  IQif0/;. 

•»  8.  Bought  a  horse  for  $130,  paid  for  its  keeping,  two 
months,  $6,  and  then  sold  it  for  $124  ;  what  per  cent,  was  my 
loss?  Ans.  S]4%. 

9.  A  merchant  made  a  profit  of  $156  by  selling  a  quantity 
of  silks  at  a  gain  of  12  per  cent.     What  was  the  cost  of  the 
silks,  and  for  how  much  were  they  sold  ?     Ans.  $1300  cost. 

Explanation. — Since  he  gained  12  per  cent.,  or  TW  of  the 
cost,  $156  must  be  TVV  of  the  cost,  which  (Case  III.  Percent- 
age), is  $1300  ;  $1300  +  $156=$1456,  selling  price. 

10.  A  grocer  bought  a  lot  of  apples,  and  sold  them  at  30 
per  cent,  profit,  by  which  he  gained  $36.60.     How  much  did 
they  cost  him,  and  for  how  much  did  he  sell  them  ? 

Ans.  Cost  $122  ;  sold  for  $158.60. 

11.  Sold  a  cargo  of  wheat  for  $16000,  at  a  profit  of  25  per 
cent.     What  was  the  cost  of  cargo  ?  Ans.  $12800. 

Explanation. — $16000  is  25  per  cent,  more  than  what 
number  ?  (Case  IV.  Percentage).  Or  thus  :  Since  I  gained 
25  per  cent,  or  TYo  =  T,  I  must  have  sold  it  for  f  of  the  cost. 

12.  Gould  &  Brown  sold  a  lot  of  goods  for  $16500,  at  a 
profit  of  33  i  per  cent.     What  did  the  goods  cost  them  ? 

Ans.  $12375. 

13.  Sold  tea  at  90  cents  per  lb.?  and  gained  20  per  cent. 
What  per  cent,  should  I  have  gained  had  I  sold  it  for  $1.00 
per  Ib.  ?  Ans.  33i%. 

Note. — This  example  involves  Case  IV.  and  Case  II.  of 
Percentage.  First  find  the  cost  and  then  the  gain  per  cent,  on 
the  cost  by  selling  for  $1.00  per  Ib. 


94  PERCENTAGE. 

.      14.  Sold  a  lot  of  books  for  $480,  and  lost  20  per  cent.  ;  for 
what  should  I  have  sold  them  to  gain  20  per  cent.  ? 

Ans.  $720. 

1/15.  If  tea,  when  sold  at  a  loss  of  25  per  cent,  brings  $1.25 
per  lb.,  what  would  be  the  gain  or  loss  per  cent,  if  sold  for 
$1.60  per  lb.?  Ans.  Loss '4$. 

16.  A  merchant  marked  a  piece  of  carpeting  25  per  cent, 
more  than  it  cost  him,  but,  anxious  to  effect  a  sale,  and  sup- 
posing he  should  still  gain  5  per  cent.,  sold  it  at  a  discount  of 
20  per  cent,  from  his  marked  price.     Did  he  gain  or  lose  ? 

Ans.  Neither. 

Explanation. — Since  the  marked  price  was  125  per  cent,  of 
the  cost,  20  per  cent,  of  the  marked  price  must  be  20  per  cent, 
of  125  per  cent,  of  the  cost,  or  25  per  cent,  of  the  cost.  125 
per  cent.— 25  per  cent.  =  100  per  cent.,  or  cost 

Or  thus : 

Since  the  marked  price  was  \  (25  per  cent.)  more  than  the 
cost,  or  f  of  the  cost,  20  per  cent.,  or  £  of  the  marked  price 
must  equal  }  of  £  =  £  of  the  cost. 

17.  My  goods  are  marked  to  sell  at  retail  at  40  per  cent, 
above  cost.     I  furnish  my  wholesale  customers  at  12  per  cent, 
discount  from  the  retail  price.     What  per  cent,  profit  do  I 
make  on  goods  sold  at  wholesale  ? 

Illustration. — Suppose  $1.00  to  be  the  basis  of  computation. 
We  shall  then  have  : 

$1.00    cost.  $1.40    retail  price. 

1.40    retail  price.  .16f  amount  to  be  deducted. 

.16}  12  per  cent,  of  1.93]  selling  price, 

retail  price.  ^.00    cost  deducted. 

.23  j  profit. 

18.  My  retail  price  for  broadcloth  is  $4.75  per  yard,  by 
which  I  make  a  profit  of  33^  per  cent.     I  sell  a  wholesale  cus- 
tomer 100  yards  at  a  discount  of  30  per  cent,  from  the  retail 
price.     What  per  cent,  do  I  gain  or  lose,  and  what  do  I  receive 
per  yard  ?  Ans.  Lose  6:',;/. 

$3.32i  per  yard. 

19.  A  merchant  asked  for  a  quantity  of  dried  fruit  22  per 
cent,  more  than  it  cost  him,  but,  being  a  little  mouldy,  he  was 


PERCENTAGE.  95 

obliged  to  sell  it  for  10  per  cent,  less  than  his  asking  price.  He 
gained  $98  by  the  transaction.  How  much  did  the  fruit  cost  ? 
For  how  much  did  he  sell  it  ?  What  was  his  asking  price  ? 

Ans.  to  last,  $1220. 

20.  I  bought  a  horse  of  Mr.  A  for  15  per  cent,  less  than  it 
cost  him,  and  sold  it  for  30  per  cent,  more  than  I  paid  for  it.     I 
gained  $15  in  the  transaction.     How  much  did  the  horse  cost 
Mr.  A  ?     How  much  did  it  cost  me  ?     For  what  did  I  sell  it  ? 

Ans.  to  last,  $65. 

21.  By  selling  Java  coffee  at  18  cents  per  pound  I  make  a 
profit  of  20  per  cent.,  for  how  much  must  I  sell  it  to  make  a 
profit  of  16f  per  cent.  ?  Ans.  17|  cents. 

22.  The  cost  of  purchasing  and  transporting  a  quantity  of 
goods  from  New  York  to  Chicago  is  9  per  cent,  of  the  first  cost 
of  the  goods.     If  a  merchant  in  Chicago  wishes  to  make  a  profit 
of  25  per  cent,  on  the  full  cost  of  the  goods,  what  per  cent,  gain 
on  the  first  cost  must  he  ask,  for  them  ?     What  amount  of 
goods  must  he  purchase  in  New  York  to  realize  a  profit  of 
$3625  on  the  first  cost  ?    W^hat  would  be  the  real  profit  on 
full  cost  ?  Ans.  to  the  last,  $2725. 

23.  What  must  be  the  asking  price  of  cloth  costing  §3.29 
per  yard,  that  I  may  deduct  12£  per  cent,  from  it,  and  still 
gain  12^  per  cent,  on  the  cost  ?  Ans.  §4.23. 

24.  I  bought  a  lot  of  coffee  at  12  cents  per  pound.     Allow- 
ing that  the  coffee  will  fall  short  5  per  cent,  in  weisrhino;  it 

O  J-  O  O 

out,  and  that  10  per  cent,  of  the  sales  will  be  in  bad  debts,  for 
how  much  per  pound  must  I  sell  it  to  make  a  clear  gain  of  14 
per  cent,  on  the  cost  ?  Ans.  16  cents. 

25.  What  must  be  the  asking  price  of  raisins  costing  §7.364 
per  box,  that  I  may  fall  10  per  cent,  of  it  and  still  gain  10  per 
cent,  on  the  cost,  allowing  10  per  cent,  of  sales  to  be  in  bad 
debts?  Ans.  $10. 

Note. — Other  problems  in  Profit  and  Loss,  involving  In- 
terest, etc.,  will  be  given  in  miscellaneous  examples. 


96  PERCENTAGE. 


COMMISSION    AND    BROKERAGE. 

ART.  77.  Money  received  for  buying  and  selling  goods  or 
other  property,  collecting  debts,  or  transacting  other  business 
of  like  nature  for  another  person  or  party,  is  called  Commission. 

Commission  is  usually  estimated  at  a  certain  per  cent,  of 
the  amount  of  the  purchase,  sale,  collection,  or  other  business 
transacted. 

A  person  who  buys  and  sells  goods,  or  transacts  other  busi- 
ness on  commission,  is  called  a  Commission  Merchant,  Agent, 
or  factor. 

When  a  person  engaged  in  the  Commission  business  lives 
in  a  foreign  country,  or  in  a  different  part  of  the  country,  he  is 
called  a  Correspondent  or  Consignee  ;  goods  shipped  to  such  a 
person  to  be  sold  are  called  a  consignment,  and  the  person  who 
sends  the  goods  a  Consignor. 

The  rate  per  cent,  of  commission,  or  the  rate  of  commission 
as  it  is  called,  varies  with  the  amount  and  nature  of  the  business. 

Brokerage  is  money  received  for  buying  and  selling  stocks, 
making  exchanges  of  money,  negotiating  bills  of  credit,  or 
transacting  other  like  business.  Like  Commission,  it  is  com- 
puted as  a  certain  percentage  of  the  amount  of  the  money 
involved  in  the  transaction.  Brokerage  upon  stocks  is  usually 
computed  upon  their  .par  value. 

ART.  78.  The  problems  in  Commission  and  Brokerage  come 
under  one  of  the  two  following  cases  : 

1.  To  find  the  commission  or  brokerage  on  any  given  sum 
at  a  given  rate  per  cent. 

KULE. — Multiply  the  given  sum  by  the  given  rate  per  cent, 
expressed  decimally. 

2.  When  the  given  amount  includes  both  the  sum  to  be 
invested  and  the  commission  or  brokerage. 

EULE. — Divide  the  given  amount  by  $1,  increased  by  the 
rate  per  cent,  of  commission  and  brokerage,  expressed  deci- 
mally; the  quotient  will  be  the  sum  to  be  invested. 


PERCENTAGE.  97 

The  commission  or  brokerage  may  be  found  by  subtracting 
the  investment  from  the  given  amount. 

E  x  a  m.  pies. 

1.  A  commission  merchant  in  New  Orleans  purchased  cotton 
for  a  manufacturer  in  ^owell  to  the  amount  of  $16576.    What 
is  his  commission  at  2j  per  cent.  ?  Ans.  $414.40. 

2.  Paid  a  broker  1  per  cent,  for  exchanging  $750  Ohio 
money  for  Eastern  funds.     How  much  was  the  brokerage  ? 

Ans.  $1.87^, 

3.  My  agent  charges  me  $25  for  collecting  $800.     What  is 
his  rate  of  commission  ?  Ans.  3  \%. 

4.  An  architect  charges  f  per  cent,  for  plans  and  specifica- 
tions, and  li  per  cent,  for  superintending  a  building  which  cost 
$32000.     What  is  his  fee  ?  Ans.  $600. 

5.  I  collected  65  per  cent,  of  a  note  of  $87.50,  and  charged 
5  per  cent,  commission.     What  is  my  commission  and  the  sum 
paid  over  ?  Ans.  to  last,  $54.03. 

6.  My  agent  in  Baltimore  has  purchased  goods  for  me  to 
the  amount  of  $1250,  for  which  he  charges  a  commission  of  If 
per  cent.     What  sum  must  I  remit  to  pay  for  goods  and  com- 
mission ?  Ans.  $1271.87|. 

7.  Sent  to  my  agent  in  Cincinnati  $765  to  purchase  a  quan- 
tity of  bacon  ;  his  commission  is  2  per  cent,  on  the  purchase, 
which  he  is  to  deduct  from  the  money  sent.      What  is  his 
commission,  and  what  does  he  expend  for  bacon  ?  • 

Ans.  to  last,  $750. 

Remark. — The  $765  sent  includes  the  sum  to  be  invested 
in  bacon  and  the  2  per  cent,  commission  on  the  money  thus  in- 
vested. For  every  102  cents  sent,  he  will  lay  out  100  cents  for 
bacon;  hence  the  $765  is  }£?-  of  the  amount  invested.  See 
Case  IV.  Percentage. 

8.  I  have  received  $11200  from  my  correspondent  in  Boston 
with  directions  to  purchase  cotton,  first  deducting  my  commis- 
sion, 2i  per  cent.     What  is  my  commission,  and  how  much 
must  I  expend  for  cotton  ?  Ans.  to  last,  $10926.829. 

9.  My  agent  at  Chicago  writes  that  he  has  purchased  for 


98  PERCENTAGE. 

me  4000  bushels  of  wheat  at  80  cents  a  bushel,  and  wishes 
me  to  send  him  a  check  on  New  York,  which  he  can  sell  to  a 
broker  for  a  premium  of  £  per  cent.  How  large  a  check  shall 
I  send  him,  his  commission  being  3  per  cent.  ? 

Ans.  $3271.464. 

10.  Field  &  Parsons  sell  for  H.  Johnson  &  Co.  3500  Ibs.  of 
butter  at  20  cts.  a  lb.,  2580  Ibs.  of  cheese  at  9  cts.  per  Jb.,  at  a 
commission  of  5  per  cent.      They  invest  the  balance  in  dry 
goods,  after  deducting  their  commission  of  2^  per  cent,  for  pur- 
chasing.    How  many  dollars  worth  of  goods  do  Johnson  &  Co. 
receive  ?     What  is  the  entire  commission  of  Field  &  Parsons  ? 

Ans.  to  last,  $863.99. 

11.  I   received   of  Brown  &  Lincoln   $560  in  uncurrent 
money  to  purchase  books.     I  pay  a  broker  3i  per  cent,  for 
current  funds,  and  invest  the  balance,  after  deducting  my  com- 
mission of  2  per  cent.     What  do  I  pay  for  books,  and  what  is 
my  commission  ?  Ans.  to  last,  $10.596. 

12.  A  broker  bought  5  shares  of  K.  K.  stock  at  35  per  cent, 
discount,  what  is  the  brokerage  at  5  per  cent.,  the  par  value  of 
each  share  being  $100  ?  Ans.  $25. 


INSURANCE. 

ART.  79.  Insurance  is  a  contract  by  which  one  party  en- 
gages, for  a  stipulated  sum,  to  insure  another  against  a  risk  to 
which  he  is  exposed. 

The  party  who  takes  the  risk  is  called  the  Insurer  or 
Underwriter,  and  the  party,  protected  by  the  insurance,  the 
Insured. 

The  sum  paid  for  obtaining  the  insurance  is  called  the 
Premium,  and  the  written  contract  is  called  the  Policy. 

Insurance  is  generally  effected  by  a  joint-stock  company 
or  by  individuals  who  unite  to  insure  each  other,  called  a 
Mutual  Insurance  Company. 

When  the  insurer  agrees  to  pay  the  insured  a  certain  sum 
of  money  if  he  is  sick,  it  is  called  Health  Insurance. 


PERCENTAGE.  99 

When  the  insurer  agrees  to  pay  to  the  heirs  of  the  insured, 
or  to  some  specified  person,  a  certain  sum  in  case  of  his  death, 
it  is  called  Life  Insurance. 

Insurance  on  property  is  either  fire  or  marine. 

Fire  Insurance  is  a  guarantied  indemnity  against  the  loss 
or  damage  of  property  by  fire.  It  is  generally  effected  for  a 
year  or  term  of  years. 

Marine  Insurance  is  a  guarantied  indemnity  against  the 
loss  or  damage  of  property  by  the  perils  of  transportation  by 
water.  Insurance  on  the  property  carried  is  called  Cargo  In- 
surance ;  that  on  #10  vessel  is  called  Hull  Insurance. 

In  Mutual  Insurance  Companies,  each  person  insured  be- 
comes a  party  to  a  certain  extent  in  the  losses  of  the  con- 
cern.  The  person  insured  pays  a  small  cash  premium  at  the 
time  the  insurance  is  effected,  and  he  also  gives  to  the  company 
premium-note,  upon  which  he  is  liable  to  be  assessed  to  the 


Amount  of  its  face.  After  a  sufficient  sum  has  accumulated 
from  the  premiums  no  further  assessments  are  made  on  the 
notes,  and  any  surplus  funds  are  distributed  among  the  mem- 
bers of  the  company. 

ART.  80.  Most  of  the  problems  in  Insurance  come  under 
one  of  two  cases. 

1.  When  the  amount  insured  and  the  rate  of  insurance  are 
given  to  find  the  Premium. 

KULE.  —  Multiply  the  amount  insured  by  the  rate  of  Insur- 
ance expressed  decimally. 

2.  To  find  for  what  sum  a  policy  must  be  taken  out,  at  a 
given  rate,  to  cover  both  property  and  premium. 

RULE.  —  Divide  the  sum  for  which  the  property  is  to  be  in- 
sured by  $1,  diminished  by  the  rate  of  insurance  expressed 
decimally.  (See  Example  13.) 

DElxa-inples. 

1.  What  is  the  premiun  for  insuring  goods  valued  at  $4500 
at  2i  per  cent.  ?  Ans.  $112.50. 

2.  A  hotel  worth  $15000  is  insured  for  f  of  its  value  at  f 
per  cent.     The  policy  and  survey  cost  $1.50  ;  what  will  be  the 
premium  ?  Ans.  $39. 


100  PERCENTAGE. 

3.  An  insurance  company  insured  a  block  of  buildings  for 
$350000  at  |  per  cent.,  but  thinking  the  risk  too  great,  they 
reinsured  $150000  of  it  at  £  per  cent,  in  another  company,  and 
$100000  of  it  at  f  per  cent,  in  another.     How  much  premium 
did  the  company  receive  ?     How  much  did  it  pay  to  both  the 
other  companies  ?     How  much  did  it  clear  ?     What  per  cent, 
of  premium  did  it  really  receive  on  the  part  not  reinsured  ? 

Ans.  to  last,  -f^  per  cent. 

Note. — All  property  in  one  block,  or  in  adjacent  buildings, 
having  communications,  or  on  one  vessel,  is  considered  as  one 
risk,  and  Insurance  Companies  seldom  take  more  than  $10000 
in  one  risk.  Some  companies  of  very  large  capital  take  $20000, 
but  small  companies  do  not  take  more  than  from  $3000  to 
$5000  in  one  risk. 

4.  A  ship  valued  at  $40000  is  insured  for  £  of  its  value  at 
H  per  cent.,  and  its  cargo,  valued  at  $36000,  at  f  per  cent. 
What  is  the  cost  of  insurance  ?  Ans.  $738. 

5.  A  merchant  paid  $1450  premium  for  the  insurance  of  a 
cargo  of  cotton,  shipped  from  New  Orleans  to  Boston,  the  rate 
of  insurance  being  2|  per  cent.     What  was  the  value  of  the 
cargo  ?  Ans.  $58000. 

6.  Paid  $7.20  for  the  insurance  of  a  house  at  f  per  cent. 
If  the  policy  and  survey  cost  $1.50,  for  how  much  was  the 
house  insured  ?  Ans.  $950. 

7.  I  pay  $50  for  an  insurance  of  goods  valued  at  $32500, 
and  shipped  from  New  York  to  St.  Louis.     What  was  the  rate 
of  insurance?  Ans.  ^%. 

8.  A  house  valued  at  $1200  has  been  insured  for  f  of  its 
value  for  3  years  at  1  per  cent,  per  annum.     Near  the  close  of 
the  third  year  it  is  destroyed  by  fire.     What  is  the  actual  loss 
to  the  owner,  no  allowance  being  made  for  interest  ? 

Note. — The  insurance  company  must  pay  him  $800  ;  but 
of  this  sum  he  has  paid  to  the  company  $24  premium  ;  hence 
he  actually  receives  but  $800-24=  $776. 

9.  My  house  was  insured  for  $45000  for  5  years     The  first 
year  I   paid  $1.50  for   policy  and   survey,  and  f  per  cent. 
premium ;  each  succeeding  year  I  paid  |  per  cent,  premium. 


PERCENTAGE.  101 

What  was  the  total  cost  of  insurance  ?  The  house  was  burned 
during  the  fifth  year ;  what  was  the  actual  loss  of  the  com- 
pany, no  allowance  being  made  for  interest  ? 

Ans.  to  last,  $43817.25. 

10.  A  merchant  ships  $31360  worth  of  wheat  from  Chicago 
to  Buffalo.     For  what  must  he  get  it  insured  at  2  per  cent,  so 
as  to  cover  both  the  value  of  the  wheat  and  the  premium  paid 
for  its  insurance  ?  Ans.  $32000. 

Explanation. — Since  the  policy  is  to  cover  both  the  value 
of  the  wheat  and  the  premium,  and,  since  the  premium  is  2 
per  cent.,  or  T|  „•  of  the  amount  covered  by  the  policy,  the  value 
of  the  wheat  must  be  TW  (or  98  per  cent.)  of  the  sum  insured. 
$31360  is  TVo  (98  per  cent.)  of  what  ?  See  Case  III.  Per- 
centage. 

11.  For  what  must  a  cargo  of  R.  R.  iron  worth  $115200 
be  insured  to  cover  both  the  value  of  the  iron  and  premium, 
the  rate  of  insurance  being  4  per  cent.  ?  Ans.  $120000. 

12.  A  merchant  shipped  a  cargo  of  flour  worth  $47880  from 
Chicago  to  San  Francisco  via  New  York.      To  insure  it  from 
Chicago  to  Buffalo  he  paid  l£  per  cent.  ;  from  Buffalo  to  New 
York  j  per  cent. ;  from  New  York  to  San  Francisco  3£  per 
cent.     For  what  sum  must  it  be  insured  to  cover  value  of  flour 
and  premium  for  the  voyage  ?  Ans.  $50400. 

13.  A  policy  covering  property  and  premium  is  taken  for 
§12045.     What  is  the  value  of  the  property  insured,  the  rate 
being  f  per  cent.  ?  Ans.  $12000. 

Explanation. — Since  the  policy  covers  both  property  and 
premium,  $12045  is  f  per  cent,  more  than  the  property.  See 
Case  IV.  Percentage. 

14.  A  merchant  insures  a  cargo  of  goods  for  $81800,  cover- 
ing both  the  value  of  the  goods  and  the  premium,     What  is 
the  value  of  the  goods,  the  rate  of  insurance  being  2{  per 
cent.  ?  Ans.  $80000. 

15.  The  owners  of  the  steamer  Florence  have,  for  the  past 
20  years,  paid  5  per  cent,  per  annum  for  her  insurance.     She 
was  sunk  this  morning.     Have  they  gained  or  lost  by  having 
the  steamer  insured  ?  Ans. 


102  PERCENTAGE. 


LIFE     INSURANCE. 

ART.  81.  Life  Insurance  is  a  contract  by  which  the  insurer 
agrees,  for  an  annual  premium,  to  pay  to  the  heirs  of  him 
whose  life  is  insured,  or  some  person  specified,  a  certain  sum 
of  money  in  case  of  his  death  during  the  time  for  which  the 
insurance  of  his  life  is  effected. 

When  the  contract  extends  only  a  given  number  of  years, 
it  is  called  a  temporary  insurance. 

The  individual  whose  life  is  insured  pays  annually,  during 
life,  a  certain  percentage  of  the  sum  for  which  his  life  is  in- 
sured. This  sum  is  called  an  Annual  Premium,  and  varies 
with  the  age  of  him  whose  life  is  insured. 

The  basis  of  the  percentage  is  the  average  number  of  per- 
sons lives  who  have  attained  to  the  uge  of  the  applicant.  This 
average  extension  of  life,  beyond  a  given  age,  is  called  Expec- 
tation of  Life.  Tables  showing  the  expectation  of  life  for 
every  year  of  man's  existence  are  deduced  from  life  statistics, 
or,  as  they  are  commonly  called,  Bills  of  Mortality. 

The  annual  premium  must  be  such  a  sum  as  will,  when  put 
at  interest,  amount  to  the  sum  insured,  at  the  close  of  the  ex- 
pectation of  life.  This  sum  is  easily  found  upon  the  principle 
of  Life  Annuities. 

Life  Insurance  Companies  have  tables  showing  the  premium 
to  be  paid  at  any  age  to  secure  an  annuity  of  $100,  during  the 
remainder  of  life.  As  the  computations  of  Life  Insurance  are 
based  upon  these  tables,  it  is  unnecessary  to  add  problems. 

There  are  two  tables  showing  the  Expectation  of  Life. 
One,  called  the  Carlisle  Table,  based  upon  Bills  of  Mortality 
prepared  in  England,  is  in  general  use  in  that  country,  and  to  a 
limited  extent  in  this.  The  other,  called  the  Wigglesworth  Table, 
prepared  by  Dr.  Wigglesworth,  from  data  founded  upon  the 
mortality  of  this  country,  is  used  to  a  considerable  extent  here. 

The  Expectation  of  Life,  according  to  the  two  tables 
named,  is  shown  in  the  following 


PERCENTAGE. 


103 


TABLE. 


1 

K\|K'ctntion  by 
C.  Table. 

\.\\  relation  by 
W.Tul.l... 

§> 

Kxpeotntion  by 
C.  Tublo. 

£. 

c  •- 
.SS 

¥. 
1* 

H 

| 

Exportation  by 
C.  Tuble. 

£ 

H 

i* 
i> 

H 

1 

.fe- 
ll 

1 

i 

£ 

jl 

2$ 

** 

•s, 

M 

0 

38.72      2S.15 

ir 

38.59 

32.70 

48 

22.80 

22.27 

72 

8.16     9.14 

1 

44.63 

36.78 

25 

37.86 

32.33 

49 

21.81 

21.72 

73 

7.72 

8.69 

2 

47.55 

38.74 

26 

37.14 

31.93 

50 

21.11 

21.17 

74 

7.33 

8.25 

3 

49.82 

40.01 

27 

36.41 

31.50 

51 

20.39 

2061 

75 

7.01 

7.83 

4 

50.76 

40.73 

28 

35.69 

31.08 

52 

19.68 

20.05 

76 

6.69 

7.40 

5 

51.25 

40.88 

29 

35.00 

30.66 

53 

18.97 

19.49 

77 

6.40 

6.99 

6 

51.17 

40.69 

30 

34.34 

30.25 

54 

18.28 

18.92 

78 

6.12 

6.59 

7 

50.80 

40.47 

31 

33.68 

29.83 

55 

17.58 

18.35 

79 

5.80 

6.21 

8 

50.24 

40.14 

32 

33.03 

29.43 

56 

16.89 

17.78 

80 

5.51 

5.85 

9 

49.57 

39.72 

33 

32.36 

20.02 

57 

16.21 

17.20 

81 

5.21 

5.50 

10 

48.82 

39.23 

34 

31.68 

28.62 

58 

15.55 

16.63 

82 

4.93 

5.16 

11 

48.04 

33.64 

35 

31.00 

28.22 

59 

14.92 

16.04 

4.G5     4.87 

12 

47.27 

38.02 

36 

30.32 

27.78 

60 

14.34 

15.45 

84 

4.39 

4.66 

13 

46.51 

37.41 

29.64 

27.34 

61 

13.82 

1486 

85 

4.12 

4.57 

14 

45.75 

36.79 

38 

28.96 

26.91 

62 

13.31 

14.26 

86 

3.90 

4.21 

13 

45.00 

36.17 

39 

28.28 

26.47 

63 

12.81 

13.66 

87     3.71 

3.90 

16 

44.27 

35.76 

40 

27.61 

26.04 

64 

12.30 

13.05 

88     3.59 

3.67 

17 

4357 

35.37 

41 

26.97 

25.61 

Co 

11.79 

12.43 

89     3.47 

3.56 

18 

42.87 

34.93 

42 

26.34 

25.19 

66 

11.27 

11.96 

90 

3.28 

3.73 

19 

42.17 

34.59 

43 

25.71 

24.77 

07 

10.75 

11.48 

91 

3.26 

3.32 

20 

34.22 

44 

25.09 

24.35 

OS 

10.23 

11.01 

92     3.37 

3.12 

21 

40.75     33.84 

45 

24.46 

23.92 

69 

9.70 

10.50 

93 

3.48 

2.40 

22 

4!)  04     33.46 

46 

23.82 

23.37 

70 

9.18 

10.06 

94 

3.53 

1.98 

23 

39.31 

33.08 

47 

23.17 

22.83 

71 

8.G5 

9.60      95 

3.53 

1.62 

TAXES. 

ART.  82,  A  Tax  is  a  sum  of  money  assessed  according 
to  law  upon  the  person  or  property  of  a  citizen,*  for  the  use  of 
the  nation,  state,  corporation,  county  or  parish,  society  or 
company. 

Taxes  upon  property  are  direct  or  indirect,  according  to 
the  manner  in  which  they  are  assessed. 

A  direct  tax  is  assessed  directly  upon  the  taxable  property 
(determined  by  law)  of  citizens,  and  is  generally  collected  an- 
nually. Taxes  are  sometimes  assessed  at  a  certain  per  cent,  of 
the  property  taxed  ;  but  more  commonly  as  a  given  number  of 
mills  on  §1. 

*  The  term  citizen  is  used  in  its  general  sense. 


104  PERCENTAGE. 

Property,  subject  to  taxation,  is  either  real  or  personal. 
Real  Property  or  Real  Estate  consists  of  lands,  mills,  houses, 
and  other  fixed  property.  All  other  property  is  called  per- 
sonal. 

The  value  of  taxable  property  is  fixed  either  by  the  owner 
under  oath,  as  in  case  of  personal  property,  or  by  an  officer 
chosen  for  the  purpose,  called  an  Assessor. 

Indirect  Taxes  are  assessed  upon  goods  imported  into  the 
country,  and  are  collected  at  their  port  of  entry.  They  are 
called  customs  or  duties. 

Remark. — Duties  are  called  indirect  taxes,  since,  according 
to  the  tenets  of  most  political  economists,  the  duty,  imposed 
upon  imported  goods  and  apparently  paid  by  the  importer, 
enhances  the  price  of  these  goods  in  market,  and  is  thus  in- 
directly and  really  paid  by  the  consumer.  Other  political 
economists,  called  Protectionists,  hold  that,  in  most  instances, 
the  protective  duty  really  cheapens  the  price  of  goods.  Such 
duties  can  hardly  be  called  taxes. 

A  tax  assessed  upon  the  person  of  citizens  is  called  a  poll 
or  capitation  tax,  since  it  is  assessed  at  so  much  per  head  (poll 
or  caput),  without  reference  to  property. 

Note. — In  some  states  poll-taxes  are  only  collected  for 
gtreet  or  road  purposes. 

Examples. 

1.  The  taxable  property  of  the  city  of  Cleveland  for  1857 
was  $21648938.     The  taxes  were  assessed  as  follows  : 

For  State  purposes,  3.1  mills  on  a  dollar. 

"    County  purposes,          2.5     " 
"    Corporation  purposes,  8.       " 

What  was  the  amount  of  tax  assessed  for  each  purpose  ? 
How  much  will  be  collected,  allowing  8  per  cent,  to  be  uncol- 
lectible ?  Ans.  to  last,  $270871.51. 

2.  The  taxable  property  of  the  city  of  B.  for  1857  was 
$35500000  ;  the  assessment  was  15  mills  on  a  dollar.     What 
was  the  total  tax  of  the  city  ?     What  tax  was  assessed  upon 
each  of  the  following  citizens  ? 


PERCENTAGE. 


105 


Mr.  A  who  paid  tax  on      $13560. 


Mr.  B 
Mr.  C 
Mr.  D 
Mr.  E 
Mr.  F 


9850.59. 
450.87. 
60850. 
119380. 
1000000. 


ART.  83.  The  labor  of  making  out  a  tax  list  may  be  less- 
ened by  using  tables. 

The  following  table  will  be  found  very  convenient  for  such 
a  purpose.  One  or  two  examples  will  illustrate  the  manner  of 
using  it.  The  table  is  easily  formed  for  any  number  of  mills 
on  a  dollar. 

TABLE. 
Kate  of  tax  15  mills  on  a  dollar. 


Prop. 

Tax.    Prop. 

Tax. 

Prop. 

Tax. 

Prop. 

Tax. 

Prop. 

Tax. 

$  1 

$.015 

$21 

$.315 

$41 

$.615 

$61 

$  .915 

$  si 

$1.215 

2 

.03 

22 

.33 

42 

.63 

62 

.93 

82 

1.23 

3 

.045 

23 

.345 

43 

.645 

63 

.945 

83 

1.245 

4 

.03 

24 

.36 

44 

.66 

64 

.96 

84 

1.26 

5 

.075 

25 

.375" 

45 

.675 

65 

.975 

85 

1.275 

6 

.09 

26 

.39 

46 

.69 

66 

.99 

86 

1.29 

7 

.105 

27 

.405 

47 

.705 

67 

1.005 

87 

1.305 

8 

.12 

28 

.42 

48 

.72 

68 

1.02 

88 

1.32 

9 

.135 

29 

.435 

49 

.735 

69 

1.035 

89 

1.335 

10 

.15 

30 

.45 

50 

.75 

70 

1.05 

90 

1.35 

11 

.165 

31 

.465 

51 

.765 

71 

1.065 

91 

1.365 

12 

.18 

32 

.48 

52 

.78. 

72 

1.08 

92 

1.38 

13 

.195 

33 

.495 

53 

.795 

73 

1.095 

93 

1.395 

14 

.21 

34 

.51 

54 

.81 

74 

1.11 

94 

1.41 

15 

.225 

35 

.525 

55 

.825 

75 

1.125 

95 

1.425 

1G 

.24 

36 

.54 

56 

.84 

76 

1.14 

96 

1.44 

17 

.255 

37 

.555 

57 

.855 

77 

1.155 

97 

1.455 

18 

.27 

38 

.57 

58 

.87 

78 

1.17 

98 

1.47 

19 

.285 

39 

.585 

59 

.885 

79 

1.185 

99 

1.485 

20 

.30 

40 

.60 

60 

.90 

80 

1.20 

100 

1.50 

Explanation  of  Table. — Suppose,  for  example,  we  wish  to 
find  the  tax  of  Mr.  A  in  the  above  example.  $13560=$13000+ 
$500 +  $60.  The  tax  on  $13000  is  found  from  the  tax  of 
$13  (.195)  by  removing  the  decimal  point  three  places  to  the 
right  ($195.)  ;  the  tax  on  $500  is  found  from  the  tax  of  $5 
(.075)  by  removing  the  point  two  places  to  the  right  ($7.50)  ; 
the  tax  on  $60  is  found  in  the  table  ($.90).  $195.  +  $7.50  + 
$.90= $203.40  ;  tax  on  $13560.  B's  tax  in  Ex.  2  is  found 


106  PERCENTAGE. 

in  the  same  manner.  Thus  :  tax  on  $9=. 135,  tax  on  $9000= 
$135  ;  tax  on  $8=. 12,  tax  on  $800=$  12  ;  tax  on  $50=.75  ; 
tax  on  59  cents  (found  from  tax  of  $59  by  removing  point  two 
places  to  the  ^)  =  .Q885=.09  nearly. 

$135. 
12.75 

J39 

Tax  on  $9850.59 =$147.84 

3.  Find  from  the  above  table  the  tax  assessed  upon 

E.  Gr.  who  paid  tax  on  $  35867.50. 
H.  E.  S.  "     "       "     "      115380. 
A.  K.     "     "       "     "     586789.99. 
R.  S.       "     "       "     "  480.48. 

4.  The  cost  of  maintaining  the  Public  Schools  of  the  city 
of  B  for  1858  is  estimated  at  $56000.      The  taxable  property 
of  the  city  is  $22400000.     How  many  mills  tax  on  a  dollar 
must  be  assessed  for  school  purposes  ?     Suppose  the  uncol- 
lectible tax  will  equal  10  per  cent,  of  the  tax  assessed  ;  how 
many  mills  on  a  dollar  must  in  this  case  be  assessed  ? 

Ans.  to  last,  2J  mills. 


DUTIES     OB     CUSTOMS. 

ART.  84.  Duties  or  Customs  are  sums  of  money  assessed 
by  government  upon  imported  goods.* 

Duties  upon  goods  are  collected  at  their  port  of  entry,  by 
officers  appointed  by  government  and  called  custom-Jwuse 
officers.  At  each  port  of  entry  for  foreign  goods  is  a  custom- 
house, where  all  custom  business  is  done. 

Duties  are  of  two  kinds,  specific  and  ad-valorem. 

Specific  duties  are  assessed  upon  goods  at  a  certain  rate  per 
tun,  hogshead,  bale,  gallon,  etc.,  without  reference  to  their 
value. 

Ad-valorem  duties  are  a  certain  percentage  of  the  cost  of 
goods  as  shown  by  the  invoice. 

*  In  some  countries  duties  are  also  assessed  upon  exported  goods. 


PERCENTAGE.  ,      107 

An  Invoice  or  Manifest  is  a  written  account  of  the  particu- 
lars of  goods  shipped  or  sent  to  a  purchaser,  consignee,  factor, 
etc.,  with  the  actual  cost  or  value  of  such  goods  made  out  in 
the  currency  of  the  place  or  country  from  whence  imported. 

The  invoice  is  exhibited  at  the  custom-house  by  the  master 
of  the  vessel,  or  the  owner  or  consignee. 

When  an  invoice  has  not  been  received,  the  owner  or  con- 
signee must  testify  to  the  fact  under  oath,  and  then  the  goods 
are  entered  by  appraisement. 

When  the  currency  of  a  country  has  a  depreciated  value 
compared  with  that  of  the  country  into  which  they  are  im- 
ported, a  consular  certificate  showing  the  amount  of  deprecia- 
tion is  attached  to  the  invoice. 

ART.  85.  In  assessing  specific  duties,  certain  allowances 
are  made,  called  draft,  tare,  leakage,  breakage,  etc.,  before  the 
duties  are  estimated. 

Draft  is  an  allowance  for  waste.  It  must  be  deducted 
before  other  allowances  are  made. 

Tare  or  Tret  is  an  allowance  for  weight  of  box,  cask,  etc., 
containing  the  goods.  It  is  generally  computed  at  a  given  rate 
per  box,  cask,  etc. 

Leakage  is  an  allowance  for  the  waste  of  liquid. 

Breakage  is  an  allowance  on  liquors  transported  in  bottles. 

Gross  Weight  is  the  weight  of  goods  before  any  allowances 
are  made. 

Net  or  Neat  Weight  is  the  real  weight  of  goods  after  the 
allowances  have  been  deducted. 

Remark. — As  specific  duties  in  the  United  States  were 
abolished  by  the  tariff-bill  of  1846,  the  examples  given  below 
will  relate  exclusively  to  ad-valorem  duties.  The  rules 
governing  the  entry  of  vessels  and  goods  are  deemed  too 
numerous  and  unimportant  to  merit  more  space. 

Note. — In  ad-valorem  duties  no  allowances  are  made  for 
draft,  tare,  or  breakage. 

Examples. 

1.  A  portion  of  the  cargo  of  the  ship  Europa  from  Liver- 
pool to  New  York  was  invoiced  as  follows  : 


108  PERCENTAGE. 

650  yds.  Broadcloth,  cost  13s.  sterling  per  yd. 

1246  yds.  Lace,  "   2s. 

1200  yds,  Coach  Lace,  "    lid.       " 

1950  yds.  Ingrain  Carpeting,   "   3s.          "  " 

2560  yds.  Drugget,  "   2s.  4d.  "  " 

The  duty  on  the  broadcloth  was  30  per  cent. ;  on  lace  25  per 
cent. ;  coach  lace  25  per  cent. ;  carpeting  30  per  cent. ;  drugget 
30  per  cent.  What  was  the  amount  of  duty  in  our  currency, 
allowing  the  pound  sterling  to  be  $4.84  ? 

Ans.  $1689.1358. 

2.  C.  Hartwell  &  Co.,  of  Baltimore,  have  imported  from 
Havana 

100  hogsheads  of  Molasses,  63  gals,  each,  cost  25  cts.  per  gal. 
50  hogsheads  of  Sugar;  500  Ibs.  each,  "  5  cts.  per  Ib. 

150  boxes  of  Oranges,  "   $2.50  per  box. 

300  boxes  of  Cigars,  "   $8  per  box. 

160  boxes  of  Bananas,  "   $1.75  per  box. 

The  leakage  of  molasses  is  2  per  cent. ;  duty  on  same  30  per 
cent.  ;  duty  on  sugar  30  per  cent.  ;  on  oranges  20  per  cent.  ; 
on  cigars  40  per  cent.  ;  on  bananas  20  per  cent.  What  was 
the  duty  on  each  article  ?  What  was  the  amount  of  duties  ? 

Ans.  $1900.05. 

3.  A  wine  merchant  in  New  York  imported  from  Havre 

100  baskets  Champagne,  at  $13  per  basket. 
80  casks  Madeira,  at  $42  per  cask. 

56  casks  Oporto,  at  $45       " 

50  casks  Sherry,  at  $25       " 

If  an  allowance  of  3  per  cent,  for  leakage  is  made  on  the  wine 
in  casks,  what  will  be  the  amount  of  duty  at  40  per  cent.  ? 
For  what  must  the  wine  be  sold. .per  basket  or  cask  to  make  a 
clear  profit  of  25  °/0  ?  Ans.  $3286.44  duty. 


PERCENTAGE.  109 


BANKRUPTCY. 

ART.  86.  Bankruptcy  is  a  failure  in  business  and  an  in- 
ability to  pay  indebtedness. 

A  Bankrupt  or  insolvent  is  a  person  who  fails  in  business 
and  has  not  means  to  pay  all  his  debts. 

An-  Assignment  is  the  transfer  of  the  property  of  a  bank- 
rupt to  certain  persons  called  assignees,  in  whom  it  is  vested 
for  the  benefit  of  creditors. 

It  is  the  duty  of  assignees  to  convert  the  property  into 
money  and  divide  the  proceeds  pro  rata  among  the  creditors, 
after  deducting  expenses. 

The  entire  property  of  an  insolvent  is  called  his  assets  ; 
and  the  amount  of  his  indebtedness  his  liabilities. 

Ex.  1.  A  merchant  failing  in  business  owes  A  $950,  B 
$2500,  C  §1500,  and  D  $3050.  His  assets  are  $6000,  and  the 
expense  of  settling  will  be  $800.  What  per  cent,  of  his  in- 
debtedness can  he  pay  ?  What  dividend  will  each  creditor 

receive  ? 

A's  claim,  $  950        $  950  x.  65=$  617.50  A'sdiv. 
B's      "        2500          2500  x.  65=    1625.00  B's   " 
•C's      "        1500          1500  x.  65=     975.00  C's   " 
D's     '-        3050          3050x.65=_1982.50D's  " 
Liabilities,  88000  Proof,  $520000 

Assets,  6000 

Expense  of  settling,       800 
Net  proceeds,  $5200 

5200.00-=-8000=.65,  or  65  per  cent. 

Explanation.  —  Since  his  liabilities  are  $8000  and  the  net 
proceeds  of  his  assets  $5200,  he  can  pay  $5200  on  $8000,  or 
65  per  cent,  of  his  liabilities.  Hence  each  creditor  can  receive 
65  per  cent,  of  his  claim. 

Note.  —  It  is  more  common  to  ascertain  how  much  can  be 
paid  on  a  dollar.  As  65  per  cent,  of  $1  is  65  hundredths  of  it, 
or  65  cents,  the  process  is  the  same. 


Divide  the  net  proceeds  of  the  assets  by  the  amount  of 


110  PERCENTAGE. 

liabilities,  and  the  quotient  will  be  the  per  cent,  of  the  indebted- 
ness (or  the  number  of  cents  on  a  dollar)  that  can  be  paid. 

To  find  each  creditor's  dividend,  multiply  his  claim  by  the 
per  cent,  thus  found. 

2.  Best  &  Foster  became  embarrassed  and  failed  in  business. 
Their  indebtedness  was  $65000.     The  firm  had  cash  and  goods 
convertible  into  cash,  $12500  ;  building  and  lot,  $40000 ;  bills 
collectible,  $2100.     If  the  expense  of  settling  is  5  per  cent,  of 
the  amount  distributed  to  creditors,  what  per  cent,  of  their 
indebtedness  can  they  pay  ?     What  will  C.  Greene  &  Co.  re- 
ceive, whose  claim  is  $25800  ?         Ans.  to  first,  80  per  cent. 

Suggestion. — Divide  assets  by  $1.05  ;  the  quotient  will  be 
net  proceeds. 

3.  C.  Smith  &  Co.  have  become  insolvent.     They  owe  A 
$3500,  B  $1500,  C  $1450,  D  $850,  E  $350,  and  F  $450. 
Their  effects  (assets)  amount  to  $4981.50.     The  charges  of  the 
assignees  will  be  2|  per  cent,  of  the  amount  distributed  to 
creditors.     What  per  cent,  of  their  indebtedness  can  they  pay? 
What  will  each  creditor  receive  ?  Ans.  to  first,  60%. 


STORAGE. 

ART.  87.  Storage  is  the  price  charged  for  the  safe  keeping 
of  goods  in  a  store  or  warehouse. 

There  is  no  uniform  method  of  computing  storage.  The 
Boards  of  Trade,  or  Chambers  of  Commerce  of  the  different 
cities,  adopt  such  rules  and  rates  for  storage  as  they  deem 
equitable.  The  charges  for  storage  are  usually,  however,  a 
certain  rate  per  month  for  each  box,  bale,  cask,  etc. 

When  goods  are  withdrawn  before  the  close  of  the  month 
no  deduction  is  made,  but  storage  is  charged  for  the  full  month. 
After  the  first  month,  for  a  part  of  a  month  less  than  one  half, 
no  charge  is  made,  but  for  a  part  greater  than  one  half,  charge 
is  made  for  a  month.  In  some  cities  all  fractional  parts  of  a 
month  are  considered  full  months. 

If,  however,  goods  are  received  and  sold  on  account,  as  in 
the  commission  business,  or  are  received  and  delivered  at  the 


PERCENTAGE.  HI 

pleasure  of  the  consignor,  an  account  is  kept,  showing  the  date 
and  number  of  casks,  etc.,  received,  and  the  date  and  number 
sold  or  delivered.  In  computing  the  storage  on  such  an  account 
it  is  customary  to  average  the  time,  and  charge  a  certain  rate 
per  month  of  30  days.  If  there  is  a  fractional  part  of  a  barrel, 
3tc.,  in  the  average,  it  is  treated  as  in  the  case  of  parts  of 
months  above. 

Examples. 

1.  What  will  be  the  storage  of  150  barrels  of  flour  at  4 
cents  per  barrel  from  May  20  to  June  6. 

150x.04=$6.  Ans. 

2.  What  will  be  the  cost  of  storing  salt  at  2  cents  per 
barrel,  received  and  delivered  as  follows  :  June  6,  1858,  120 
bbls.  :  June  16,  140  bbls. ;  June  26,  200  bbls.  ;  July  5^  300 
bbls  ;  July  16,  180  bbls.  ;  July  20,  160  bbls.     AU  delivered 
Aug.  1. 

Operation. 

1858.  bbl.     d.       prod. 

June    6.  Kec'd.    120x10=  1200 
"     16.       "        140 

^60x10=  2600 
"    26.       "        200 

~860X   9=  7740 
July    5.       "        300 

1160x10=11600 
"    15.       "        18P 

1340  x   5=  6700 
"     20.       "        160 

1500x11=16500 
Aug.    1.  Deliv.  1500 

30)46340 
Bbls.  chargeable  for  1  month,  1544| 

1545x.02=$30.90,  storage. 

Explanation. — The  storage  of  120  bbls.  for  10  d.  is  the 
same  as  the  storage  of  1200  barrels  for  1  day  ;  the  storage  of 
260  for  10  days,  the  same  as  the  storage  of  2600  bbls.  for  1  day, 
and  so  on.  Hence  the  amount  of  storage  is  1200+2600  +  7740+ 
11600+6700  +  16500  bbls.=46340  bbls.  for  1  day=4635  (f 
called  1  bbl.)  bbls.  for  1  month. 


112 


PERCENTAGE. 


3.  What  will  be  the  storage  of  flour  at  5  cents  per  bbl.  per 
month,  received  and  delivered  as  follows  ? 

Keceived  July  1,  1858,  400  bbls. ;  July  15, 350  bbls. ;  July 
26,  450  bbls.  Delivered  July  12,  200  bbls. ;  July  20,  400 
bbls. ;  Aug.  1,  200  bbls. ;  and  Aug.  8,  400  bbls. 

Operation. 
1858. 


July    1. 
"   12. 

"   15. 
"  20. 
"  26. 
Aug.    1. 
Aug.   8. 

Kec'd. 
Deliv. 
Bal. 
Kec'd. 
Bal. 
Deliv. 

400  x 
200 

11=  4400 
3=     600 
5=  2750 
6=     900 
6=  3600 
7=  2800 

200  x 
350 

"550  x 
400 

Bal. 
Kec'd. 

150  x 

450 

Bal. 
Deliv. 

600  x 
200 

Bal. 
Deliv. 

400  x 
400 

30)1505.0 
Bbls.  chargeable  1  month,    502 

502  x.  05=  $25.10  Ans. 

Explanation.—  "From  July  1  to  July  12,  400  bbls.  were 
stored  ;  from  July  12  to  July  15,  200  bbls.  ;  from  July  15  to 
July  20,  550  bbls.  ;  from  July  20  to  July  26,  150  bbls.  ;  from 
July  26  to  Aug.  1,  600  bbls.  ;  from  Aug  1  to  Aug.  8,  400  bbls. 


Commencing  with  the  first  date  and  ending  with  the  last, 
multiply  the  number  of  barrels,  or  other  articles  in  store,  from 
each  date  to  the  one  NEXT  following  it,  ~by  the  number  of  days 
between  these  dates.  Divide  the  sum  of  the  several  products 
by  30,  and  the  quotient  will  be  the  number  of  articles  stored  for 
one  month,  and  this  number  multiplied  by  the  rate  of  storage 
for  each  article  ivill  give  the  amount  of  storage  charged. 

Remark.  —  The  following  form  will  give  the  student  a  very 
good  idea  of  an  Account  of  Storage.  The  form  can  be  filled 
by  the  process  used  in  solving  Ex.  3. 

4.  Storage  of  goods  on  account  of  C.  T.  Wilder  &  Co., 


PERCENTAGE. 


113 


Chicago,  111.,  at  5  cents  a  bbl.  per  month,  by  Hubby  &  Hughes, 
Cleveland,  0. 

KECEIVED.  DELIVERED. 


1858. 

Bbla. 

Balance  on  hand. 

Days. 

Products. 

1858. 

Bbls. 

Jan. 

1    350 

Jan. 

20 

700 

tt 

12   650 

tt 

31 

200 

Feb. 

5   500 

Feb. 

24 

800 

« 

10 

•320 

Mar. 

20 

350 

tt 

28 

440 

it 

25 

700 

Mar. 

15 

850 

Apr. 

5 

400 

«     J30 

200 

it 

8 

100 

What  is  the  storage  on  the  above  account,  closed  April  12, 
1858,  and  how  many  barrels  are  on  hand  ? 

ART.  88.  Butchers  and  drovers  sometimes  hire  their  cattle 
pastured  or  fed  on  account,  entering  and  withdrawing  them  as 
circumstances  may  require.  The  account  is  closed  in  the  same 
manner  as  an  account  of  storage. 

Account  of  pasturage  of  cattle  at  60  cents  a  head  per  week 
for  Lewis  &  Vincent,  Portsmouth,  0.,  by  John  Goodwin, 
Wayne,  tp. 

KECEIVED.  WITHDRAWN. 


1858. 

Head. 

Balance  on  hand. 

Days. 

Products. 

1858. 

Head. 

June 

3 

9 

June 

5 

2 

u 

10 

5 

u 

7 

4 

(C 

18 

15 

it 

12 

5 

July 

1 

20 

it 

15 

3 

tt 

9 

10 

1C 

21 

10 

(i 

31 

5 

July 

3 

10 

Aug. 

3 

12 

tt 

12 

10 

u 

16 

13 

it 

20 

6 

it 

31 

10 

tt 

28 

2 

Sept. 

25 

9 

Aug. 

7 

5 

a 

30 

3 

n 

13 

15 

Oct. 

1 

8 

tt 

20 

9 

Sept. 

28 

10 

Oct. 

4 

5 

tt 

8 

10 

it 

15 

13 

What  is  the  average  number  of  cattle  pastured  each  week  (7 

days),  and  what  is  due  John  Goodwin  ?   Ans.  to  last,  $159. 

8 


114  PERCENTAGE. 


GENERAL     AVERAGE. 

ART.  89.  When,  for  the  safety  of  a  ship  in  distress,  any 
destruction  of  property  or  expense  is  necessarily  and  voluntarily 
incurred,  either  by  cutting  away  the  masts,  throwing  goods 
overboard,  or  otherwise,  all  persons  who  have  goods  on  board, 
or  property  in  the  ship,  bear  their  proportion  of  the  loss. 

The  method  of  apportioning  the  loss  among  the  several  in- 
terests, sacrificed  or  benefited  by  the  sacrifice,  is  called  General 
Average,  and  the  property  thus  sacrificed  is  called  Jettison. 

In  ascertaining  the  amount  of  loss  to  be  averaged,  not  only 
the  amount  of  goods  thrown  overboard  is  considered,  but  also 
all  damages  to  the  ship,  cost  of  repairs,  and  expense  of  deten- 
tion for  making  repairs,  including  the  wages  of  officers  and 
crew  ;  also  the  expense  of  entering  a  harbor  to  avoid  peril,  or 
of  setting  afloat  when  stranded  ;  also  towage  in  case  of  being 
disabled,  or  salvage  paid  another  vessel  for  affording  relief,  etc. 

When  the  repairs  made  consist  of  new  masts,  rigging,  etc., 
a  deduction  of  |  of  their  cost  is  usually  made,  since  they  are 
considered  better  than  the  old. 

In  estimating  the  value  of  the  three  contributing  interests — 
vessel,  freight,  and  cargo — it  is  customary  to  value  the  cargo 
at  the  price  it  would  have  brought  at  its  port  of  destination. 
It  is  sometimes  valued  at  its  invoice  price  at  the  port  of  lading. 

As  the  wages  of  seamen,  pilotage,  etc.,  are  paid  out  of  the 
freight,  a  deduction  is  made  from  the  gross  freight  for  this 
purpose.  The  amount  to  be  deducted  is  not  determined  in  a 
uniform  manner.  According  to  some  authorities,  the  gross 
freight  less  1  is  the  net  freight,  except  in  New  York,  where  | 
is  deducted.  The  general  practice,  however,  is  to  ascertain 
what  sum  will  actually  be  left  to  the  vessel  as  net  freight,  after 
paying  seamen's  wages,  etc.  Sometimes  the  vessel  earns  a  net 
freight  of  f  the  total  amount,  and  sometimes  the  seamen's 
wages,  etc.,  absorb  the  whole  of  a  very  low  freight.  Each  case 
is  estimated  by  its  attendant  circumstances. 


PERCENTAGE.  115 

The  practical  difficulty  in  General  Average  is  to  determine 
whether  the  loss  is.  subject  to  a  general  average.  In  some  cases 
the  loss  is  borne  by  only  a  part  of  the  contributory  interests. 

When  either  a  part  or  the  whole  of  the  ship  or  cargo  or 
both  is  insured,  the  insurers  bear  their  proportion  of  the  loss  as 
found  by  average.  (See  Ex.  1.)  In  some  instances  the  adjust- 
ment of  the  insurance  becomes  a  very  intricate  problem. 


Divide  the  total  loss  subject  to  average  by  the  sum  of  the 
values  of  the  contributory  interests,  and  multiply  each  interest 
by  the  percentage  thus  found. 

Note.  —  The  jettison  must  be  included  in  the  contributory 
interests,  and  bear  its  proportion  of  the  loss. 

IS  x  a  m  pies. 

1.  The  ship  Western  World,  in  her  passage  from  New- 
York  to  Aspinwall  was  struck  by  a  severe  gale  near  the  island 
of  Cuba.  After  throwing  overboard  cargo  amounting  to  $4650, 
she  made  the  port  of  Havana.  Here  the  cost  of  the  necessary 
repairs  of  the  vessel  was  $1800,  and  the  cost  of  detention  in 
port  $450Voi  The  contribilcory  interests  were  as  follows  :  value 
of  ^  ship  $35$)0;  value  of  cargo  $24000;  net  freight  $4000. 
Of  the  cargo,  $8500  was  shipped  by  Terry  &  Wheeler  ;  $7500 
by  Morse  &  Duty  ;  $5000  by  T.  C.  Hood  &  Co.  ;  and  $3000 
by  P.  Kinney  &  Co.  How  ought  the  loss  to  be  averaged  ? 

Operation. 

Vessel,      .....     $35000          Jettison,  .     .     .     $4650 
Cargo,      .....       24000  Repairs,  less  1,  .       1200 

Net  freight,       .     .     .         4000  Cost  of  detention,  __450 

Total  contrib.  interests,  $63000        JTotal  loss,    .     .     $6300 

6300.00-=-63000=.10  ;  3oss  10  Per  cent- 
$35000  x  .10=|3500,  loss  borne  by  ship. 
,     24000  x.  10=  2400,    "        "     "   cargo. 
4000x10=     400,    "        "     «   freight. 
8500  x.  10=     850,    "        «     «    Terry  &  Wheeler. 
7500x10=     750,    "        «     «   Morse  &  Duty. 
5000  x  10=     500,    "        "     «   T.  C.  Hood  &  Co. 
3000x10=-     300,    "        «     "   P.  Kinney  &  Co. 


116  PERCENTAGE. 

2.  The  steamship  Asia  sailed  from  Liverpool  to  Boston  with 
a  cargo  as  follows  :  shipped  by  T.  S.  Foot  &  Co.  $45500  ;  by 
C.  S.  Moore  &  Co.  $10500  ;  by  T.  Hope  &  Sons  $7450  ;  by  C. 
White  &  Co.  $12550.  During  a  storm  the  captain  was  obliged 
to  throw  overboard  cargo  amounting  to  $8500,  and  the  neces- 
sary repairs  of  the  ship  cost  $2700.  In  addition  to  repairs,  the 
charges  for  seamen's  board,  dockage,  etc.,  were  $500.  How  is 
the  loss  to  be  shared,  the  value  of  the  ship  being  $40000,  and 
the  net  freight  $4000  ?  Ans.  Loss,  %. 

JKemarJc. — The  following  examples  will  give  the  student 
some  idea  of  Insurance  as  connected  with  General  Average. 

3.  The  schooner  Michigan  sailed  from  Chicago  for  Buffalo 
with  the  following  cargo  :  25000  bushels  of  wheat  owned  by 
Smith  &  Dewy ;  18500  bushels  of  corn  owned  by  Fisk  & 
Hunter  ;  850  barrels  of  flour  owned  by  T.  Ford  &  Co.  The 
schooner  is  insured  in  company  A  for  $30000,  which  is  f  of  its 
value,  at  3  per  cent. ;  the  wheat  in  company  B  for  $22500 
(invoice  price)  at  2  per  cent.  ;  the  corn  in  company  C  for 
$9250  (invoice  price)  at  li  per  cent. ;  and  the  flour  in  com- 
pany D  for  $4250  (invoice  price)  at  2|  per  cent.  The  gross  * 
freight  was  $6000,  and  seamen's  wages,  etc.,  £  of  the  gross 
freight.  During  a  severe  storm  the  flour  was  thrown  overboard. 
How  is  the  loss  to  be  borne  ?  How  is  the  payment  of  the  sum 
for  which  the  flour  is  insured  to  be  adjusted  ? 

Explanation. — By  general  average  we  find  that  the  average 
loss  is  5  per  cent.,  and  that  the  schooner  must  sustain  $2250 
of  the  loss  ;  the  cargo  $1800  ;  and  the  freight  $200.  Insur- 
ance Company  A  must  pay  5  per  cent,  of  $30000 =$1500 ; 
company  B  5  per  cent,  of  $22500 =$1125  ;  company  C  5  per 
cent,  of  $9250= $462.50  ;  and  company  D  5  per  cent,  of 
$4250= $212.50. 

4.  Suppose,  in  the  above  example,  that  when  the  schooner 
reached  her  dock  in  Buffalo  the  flour  could  have  been  sold  for 
$6120  ;  the  wheat  for  $35780  ;  the  corn  for  $11100.  How  is 
the  insurance  to  be  adjusted  ? 


INTEREST.  117 


INTEREST. 

ART.  90.  Interest  is  the  compensation  allowed  for  the  use 
of  money  or  capital. 

It  arises  from  voluntary  loans,  from  certain  investments 
giving  a  periodical  income,  and  from  delay  in  payment  of  debts 
already  due. 

The  principal  is  the  sum  loaned,  or  the  debt  on  which  in- 
terest is  paid. 

The  amount  is  the  principal  and  interest  taken  together. 

The  rate  of  interest  is  fixed  by  mutual  agreement  or  by 
law  ;  and  is  the  ratio  between  the  principal  and  interest  for  an 
assumed  length  of  time,  expressed  by  percentage  ;  thus,  "  6  per 
cent,  per  annum,"  declares  the  interest  for  one  year  to  be  T£T 
of  the  principal  In  expressing  the  rate  per  cent.,  one  year  is 
generally  assumed ;  though  in  discounting  "  short  paper/'  a 
month  is  frequently  used  ;  as  1  per  cent,  per  month. 

Usury  formerly  was  synonymous  with  interest,  but  now 
signifies  illegal  interest.  England  having  abolished  all  usury 
laws,  has  no  further  use  for  that  term.  The  practicability  of 
voluntary  contracts  in  loaning  money,  restricted  only  as  other 
contracts  are  restricted,  is  gaining  increased  favor  among  intelli- 
gent political  economists,  and  not  the  least  among  money  bor- 
rowers. When  the  rate  has  not  been  previously  agreed  upon, 
a  legal  rate  is  desirable,  to  avoid  contention  or  oppression. 
Government  regulates  all  weights  and  measures,  but  not  the 
prices  of  the  articles  weighed  and  measured.  So  it  regulates  the 
weight  and  fineness  of  coins,  but  it  should  not  dictate  the  price 
paid  for  the  use  of  them.  The  injustice  of  restricting  the  rate 
of  interest  may  be  seen  by  applying  the  principal  to  insurance 
companies.  If  the  premium  for  insurance  be  restricted  to  a  low 
rate,  only  the  safest  risks  would  be  taken,  those  having  greater 
risks  could  not  be  accommodated.  So  in  restricting  the  rate 
of  interest,  only  the  rich  and  those  who  could  offer  the  best 


118  INTEREST. 

securities  would  be  able  to  borrow  money.  If  the  loan  be  made 
at  higher  than  the  legal  rate,  the  rate  must  be  raised  still  higher 
to  cover  the  risk  arising  from  illegality. 

ART.  91.  INTEREST  may  be  simple,  annual,  or  compound. 

In  simple  interest  the  principal  alone  draws  interest ;  which 
as  it  accrues  remains  unchanged  until  ultimate  payment. 

In  annual  interest  the  interest  on  the  principal  due  at  the 
end  of  each  successive  year  becomes  a  new  principal  to  draw 
simple  interest  until  payment.  When  interest  is  made  payable 
semi-annually  or  quarterly,  the  interest,  if  not  paid,  is  convert- 
ible at  those  periods  into  the  principal,  as  in  annual  interest. 

In  compound  interest  the  entire  amount  due  at  regular  in- 
tervals of  time,  both  of  principal  and  interest,  is  converted  into 
one  new  principal.  It  is  thus  compounded  annually,  semi- 
annually,  or  quarterly. 

Note. — The  difference  between  simple,  annual,  and  com- 
pound interest  in  their  effect  depends  upon  the  time  when  in- 
terest money,  if  not  paid,  begins  to  draw  interest.  In  general  a 
debt  should  begin  to  draw  interest  as  soon  as  it  is  due.  The 
time  when  a  debt  of  interest  becomes  due  is  conventional.  In 
bank  discounts  it  is  payable  in  advance.  In  simple  interest  it 
is  not  considered  due  until  the  ultimate  payment  of  the  prin- 
cipal. In  annual  interest  it  is  due  after  it  has  been  accruing 
for  one  year,  except  the  interest  on  interest,  which  is  not  due 
till  ultimate  payment.  Compound  interest  supposes  all  in- 
terest, whether  upon  principal  or  interest,  to  be  due  at  the  end 
of  equal  successive  intervals  of  time,  generally  of  one  year  or 
six  months.  When  the  interest  is  considered  due  the  instant 
it  has  accrued,  and  all  interest  is  made  to  draw  interest,  it  is 
called  instantaneous  compound  interest.  The  actual  difference 
between  even  instantaneous  compound  interest  and  simple  in- 
terest is  not  so  great  as  at  first  might  be  supposed.  For  6$ 
simple  interest  for  one  year  will  amount  to  more  than  5f$  in- 
stantaneous compound  interest. 


INTEREST.  119 


SIMPLE     INTEREST. 

ART.  92,  Inasmuch  as  the  interest  varies  directly  as  the 
principal,  rate  per  cent.,  and  time,  these  four  terms  bear  such 
a  relation  to  each  other,  that  any  three  of  them  being  given 
the  fourth  may  be  found.  To  find  the  interest  is  by  far  the 
most  common  problem,  and  may  be  obtained  by  the  following 


GJ-E2STER-AL 

I.  Find  the  interest  for  one  year  by  multiplying  the  prin- 
cipal by  as  many  hundredths  as  are  expressed  in  the  rate  per 
cent.,  then  multiply  by  the  number  of  years  and  fractional  parts 
of  years  expressed  in  the  given  time. 

Note.  —  When  the  time  is  expressed  in  months  and  days,  it 
is  usual  for  convenience  to  regard  each  month  as  TV,  and  each 
day  as  ?J7  of  the  year.  (See  Art.  95). 

Ex.  What  is  the  simple  interest  of  $844.50  for  2  yrs.  3  mo. 
6  da.  at  1%  ? 

$844.50 
_  .07 

1  yr.  =  $59.1150 

2  yrs.=  $118.230 
3mo.=  i                -     14.779 
6d.    =Fv  _  .985 

$133.99  Ans. 

Remark.  —  The  multiplication  may  be  performed  by  aliquot 
parts.  The  fractional  parts  of  mills  may  be  neglected  when  less 
than  a  half  —  otherwise,  they  should  be  counted  as  one. 

The  following  rules  may  be  found  convenient  in  practice, 
and  the  pupil  should  become  familiar  with  the  principle  of  all, 
to  apply  that  one  which  will  give  the  result  with  the  least 
work. 

KULE  II.  —  Set  dozen  the  entire  number  of  months  in  the 
time  as  decimal  hundredths,  and  one  third  of  the  number  of 
days  as  decimal  thousandths;  multiply  half  the  principal  by 
this  number.  The  result  ivill  be  the  interest  at  §f0  per  annum. 


120 


INTEREST. 


For  4  per  cent,  subtract  £.  For  7  per  cent,  add  j. 

tt     ^1      a  a  u    g        a  a      ^ 

a     K        a  a  i  a  if)        u  a      2 

j  ¥.  -LU      ,  -3. 

Or  in  general,  for  other  rates  than  6$,  increase  or  diminish  the 
result  obtained  by  the  rule  in  the  same  ratio  that  the  rate  is 
increased  or  diminished. 

Taking  the  last  example,  we  have  by  this  rule  the  following 
solution : 

$422.25x0.272=$114.852=: the  interest  at  6$. 
Adding  1,  $133.99  =  the  interest  at  1%. 

RULE  III. — Take  one  per  cent,  of  the  principal  for  the  in- 
terest for  tivo  months  or  sixty  days  ;  then  by  aliquot  parts  find 
the  interest  for  the  given  time. 

Note. — It  will  be  observed  that  the  interest  for  6  days  may 
be  found  by  removing  the  decimal  point  three  places  to  the  left. 
For  any  multiple  of  6  days  the  result  may  be  obtained  by  a 
simple  multiplication. 

This  rule  is  convenient  in  cases  of  "short  paper/'  as  in 
bank  discounts,  which  generally  run  30,  60,  or  90  days. 

When  not  expressed,  the  rate  is  understood  to  be  $%  per 
annum. 

Ex.  What  is  the  interest  of  $420  for  30,  60,  and  90  days, 
respectively,  days  of  grace  included  ? 

60  d.  \%        =  $4.20(1)  Add  (2)  and  (3)   ,   =$2.31 =int.  33d. 

30  d.  take  J  =   2.10(2)    "    (l)and(3)       =  4.41 =int.  63d. 

3  d.  take  TV=     .21  (3)    "    (1)  (2)  and  (3)-=   6.51=int.  93d. 

By  this  analysis  most  examples  in  banking  may  be  wrought 
mentally. 

Examples. 

ART.  93.  To  be  wrought  by  each  of  the  three  rules  given 
above.  Find  the  simple  interest  of 

1.  $120  for  1  yr.  2  mo.  12  d.  at  6^  ?  Ans.  $8.64. 

2.  $340.50  for  2  yrs.  3  mo.  15  d.  at  %  ?  Ans.  $70.23. 

3.  $1000.25  for  1  yr.  9  mo.  3  d.  at  10$  ?  Ans.  $175.86. 

4.  $25  for  3  mo.  3  da.  at  12$  ?  Ans.  $.78. 
/  5.  $145.20  for  1  yr.  11  mo.  29  d.  at  1%  ?  Ans.  $20.30. 


INTEREST.  121 

•/  6.  $450  for  3  yrs.  2  mo.  21  d.  at  8^  ?         Ans.  $116.10. 
P    7.  If  a  man  borrows  $10000  at  6$  interest,  and  loans  it  at 
10$,  what  will  be  gain  in  2  yrs.  3  d.  ?  -4/w.  $803.33. 

8.  A  merchant  bought  400  yards  of  cloth  at  $4  per  yard, 
payable  in  6  months,  and  immediately  sold  it  at  $4.10,  giving 
a  credit  of  3  months,  at  the  expiration  of  which  term  he  antici- 
pated the  payment  of  his  own  paper,  getting  a  discount  off  of 
10$  per  annum.     What  did  he  gain  by  the  transaction  ? 

9.  A  merchant  bought  400  yards  of  cloth  at  $4  per  yard, 
payable  in  3  months,  and  after  holding  it  for  15  days  sold  it  at 
$4.25  per  yard,  receiving  therefor  a  note  payable  in  4  months. 
When  the  purchase  money  became  due,  he  had  this  note  dis- 
counted at  the  bank  to  meet  k.     What  did  he  gain  by  the 
transaction  ? 

10.  Taking  the  conditions  of  the  last  example,  what  would 
he  have  gained  if  he  had  borrowed  at  6%  interest,  until  the 
maturity  of  the  note  he  had  received,  sufficient  to  pay  for  the 
cloth,  and  why  should  there  be  any  difference  in  the  results  ? 

11.  If  I  invest  $1000  in  wool,  pay  5%  for  freight,  and  sell 
at  15$  advance  on  cost  price,  giving  4  months  credit,  get  this 
paper  discounted  at  the  bank  at  6%  interest,  and  repeat  the 
operation  every  15  days,  investing  all  the  proceeds  each  time, 
what  shall  I  gain  in  2  months  ? 

12.  If  a  man  borrows  $1000  at  10$  interest,  and  with  it 
buys  a  note  for  $1100,  maturing  in  5  mo.,  but  which  not  being 
paid  when  due  runs  1  yr.  6  mo.  beyond  maturity,  drawing  6$ 
interest,  will  he  gain  or  lose,  and  how  much  ? 

Ans.  He  gains  $7.33. 

13.  Jan.    1st.   a  man  borrowed   $10000  at   6$  interest. 
Fifteen  days  after  he  lent  $4500  for  8  mo.  15  d.,  without  grace, 
at  10$.     Feb.  1st,  with  the  balance  he  purchased  a  note  for 
$5650,  due  July  4,  which  not  being  paid  at  maturity  was 
extended  until  the  loan  of  $4500  became  due,  at  the  rate  of 
8$  interest.      Both  notes  having  been  then  promptly  paid,  he 
immediately  purchased  a  7$  State  Bond  of  $10000,  which, 
with  its  semi-annual  interest,  would  mature  Jan.  1st  following, 
for  which  he  paid  1$  premium  upon  its  par  value,  at  the  same 


122  INTEREST. 

time  loaning  the  balance  at  the  rate  of  1  \%  per  month.     What 
was  his  profit  for  the  year  ?  Ans.  $249.49. 

ART.  94.  To  find  the  interest  for  days,  counting  365  days 
for  a  year,  the  only  strictly  accurate 


Reduce  the  whole,  time  to  days,  by  which  multiply  the  year's 
interest,  and  divide  by  365.  Or, 

fieduce  the  actual  number  of  days  to  months  of  30  days 
each,  then  find  the  interest  by  Kule  II,  subtracting  from  the 
result  thus  obtained  TV  part  °f  itself. 


Examples. 

1.  Find  the  simple  interest  of  $1000  from  April  1  to  Dec.  1. 
Solution.—  -244  x  $60~365=Ans.  $40.11. 

2.  Find  the  simple  interest  of  $125  from  April  1  to  Dec.  7. 
Solution.—  -246   days  =  8  mo.   6  d.     Then   $125  x  .041  = 

$5.125,  and  $5.125—  ^r=  $5.055,  the  interest  required. 

By  the  first  rule  we  have  the  following  equation  :  246  x 
$7.50-^365=  $5.055. 

3.  Find  the   interest  of  $1250  for  360  days  at  6%  pel 
annum  of  365  days. 

Solution.—  T£T  of  $1250=$75.  Then  $75-  3  f  T  (or  T\)  of 
$75  :=  $73.97. 

4.  Find  the   interest  of  $1250   for   365  days  at  $%  per 
annum  of  360  days. 

Solution.—^  of  $1250=$75.  Then  $75-f  ^f  ¥  (or  TV)  of 
$75=$76.04. 

5.  What  would  be  the  diiference  between  the  accrued  in- 
terest for  90  days  on  $1000000  of  6%  State  Bonds,  computed 
first  in  Ohio,  counting  360  days  for  a  year,  then  in  New  York, 
counting  365  days  for  a  year  ?  Ans.  $205.48. 

Note.  —  In  New  York  the  interest  for  years  and  months  is 
computed  in  the  usual  way  without  reducing  to  days,  but  for 
the  odd  days  the  interest  is  computed  by  the  above  rule. 

6.  A  note  for  $1000  runs  from  Jan.  1,  1856,  to  Jan.  25, 
1858,  with  interest  at  6$.     What  amount  is  due  according  to 


INTEREST.  123 

the  above  rule  ?  What  amount  is  due  computed  as  it  would 
be  in  New  York  ?  What  amount  is  due  computed  as  it  would 
be  in  Ohio  ? 


COMPUTATION   OF  TIME   IN    INTEREST. 

ART.  95.  While  most  of  the  States  have  enacted  rigid  laws 
against  taking  usurious  interest,  they  have  left  the  mode  of 
computing  legal  interest  very  indeterminate.  Nearly  all  the 
rules  in  common  use  in  this  country  are  inaccurate  and  illegal, 
and  have  only  been  sustained  by  ^decisions  based  upon  custom ; 
but  custom  varies,  and  the  legal  decisions  have  not  been  uni- 
form. 

The  difficulties  attending  this  question,  which  has  occasioned 
so  much  litigation  and  jeopardized  so  much  capital,  can  be 
briefly  stated. 

The  fundamental  principle  upon  which  lawful  simple  in- 
terest is  computed  is  that  the  rate  should  be  exactly  propor- 
tionate to  the  term  for  which  interest  is  paid.  The  time 
usually  assumed  for  fixing  the  rate  is  one  year,  e.  g.,  6  per 
cent,  per  annum  ;  that  is,  when  the  time  is  one  year,  the  in- 
terest should  be  T£7  of  the  principal ;  and  when  the  time 
varies  from  one  year,  the  proportion  of  interest  should  vary  in 
exactly  the  same  ratio.  If,  then,  we  assume  that  the  year 
consists  of  365  days  (as  that  is  regarded  in  law  a  civil  year), 
it  must  be .  admissible,  in  computing  the  interest  on  a  note 
running  from  Jan.  1,  1856,  to  Jan.  1,  1857,  to  add  one  day's 
interest  to  the  interest  for  one  year  ;  for  in  the  case  proposed, 
February  of  a  leap  year  intervening,  the  time  was  366  days  in- 
stead of  365,  the  legal  civil  year. 

One  year  being  the  standard  of  reference  in  expressing  the 
rate,  all  time  in  computing  interest  must  be  expressed  in  years 
or  aliquot  parts  of  the  year.  But  the  year  has  no  exact  natural 
or  artificial  subdivisions  except  the  day,  and  the  day  is  an  ali- 
quot part  only  as  we  assume  the  year  to  consist  of  a  definite 
number  of  days.  The  number  360  being  a  multiple  of  more 


124  INTEREST. 

whole  numbers  than  365,  for  convenience  in  reckoning  it  would 
have  been  better  to  assume  360  days  for  the  nominal  year  in 
fixing  the  rate,  rather  than  365.  The  time  in  expressing  the 
rate  is  arbitrary,  and  as  neither  360,  365,  nor  366  is  the  exact 
number  of  days  in  all  years,  either  civil  or  astronomical,  would 
not  the  increased  facility  in  computation,  and  the  perfect  ac- 
curacy in  the  result,  warrant  the  change  ? 

The  division  of  the  year  into  twelfths,  called  months,  is 
purely  imaginary  ;  for  no  month,  either  lunar  or  calendar,  was 
ever  known  which  occupied  just  one- twelfth  of  a  year.  Mani- 
festly, if  we  assume  a  year  of  365  days  as  the  standard  for  refer- 
ence in  expressing  the  rate,  we  never  can  introduce  the  denom- 
inations of  months  in  any  form  whatsoever  without  inaccuracy, 
unless  we  involve  in  the  calculation  fractional  parts  of  days, 
which  would  be  as  absurd  as  it  would  be  difficult. 

If,  however,  we  assume  a  year  of  360  days,  we  may  have 
assumed  months  of  30  days.  Then  6  per  cent,  per  annum  of  360 
days  would  be  1  per  cent,  for  60  days,  and  all  time  being  reduced 
to  days  or  months  of  30  clays  each,  or  years  of  360  days  each,  the 
computation  would  be  simple,  rapid,  and  perfectly  accurate.  As 
it  is,  the  law  having  accurately  determined  when  a  paper  matures, 
however  the  time  may  be  expressed  in  the  paper,  the  only  accurate 
rule  for  computing  interest  is  to  ascertain  the  actual  number 
of  days,  and  make  each  day's  interest  ^ ^  of  the  annual  interest. 
Some  banks  are  restricted  by  their  charters  in  their  discounts 
to  "  6$  per  annum,"  but  are  allowed  to  compute  by  Hewlett's 
Tables.  But  Hewlett's  rule  "  To  find  bank  interest/'  makes 
all  time  reducible  to  days,  and  the  interest  for  each  ¥|¥  of  the 
year's  interest,  so  that  when  the  time  in  the  note  to  be  dis- 
counted reads  "  two  months,"  the  interest  for  T\  of  the  year 
should  never  be  taken  except  when  February  29th  of  a  leap 
year  is  included  in  the  term,  for  in  that  case  only  will  the 
"  two  months"  contain  just  60  days  and  no  more.  In  all  other 
cases,  the  interest  should  be  59,  61,  or  62-360ths  of  the  year's 
interest,  according  to  the  actual  number  of  days  contained  in 
the  time  of  the  note.  In  Massachusetts  and  some  other  States 
interest  computed  on  the  supposition  that  360  days  make  the 


INTEREST.  125 

year  is  regarded  valid.     But  in  New  York  each  day's  interest 
must  be  only  ^  of  the  year's  interest. 

ART.  96.  KULES  FOR  COMPUTING  THE  DIFFERENCE  OF 
TIME  BETWEEN  DATES — Besides  counting  the  exact  number 
of  days  as  referred  to  above,  two  rules  are  in  common  use. 

RULE  I. — By  compound  subtraction,  reckoning  30  days  for 
a  month. 

RULE  II. — By  finding  the  number  of  entire  calendar  months 
from  the  first  date,  and  counting  the  actual  number  of  days 
left. 

Note. — By  "  calendar  month"  is  meant  the  time  from  any 
day  of  one  month  to  the  corresponding  day  of  the  next  month. 
If  the  days  of  the  first  month  is  a  higher  number  than  the 
greatest  number  of  days  in  the  last  month,  the  calendar  month 
ends  with  the  last  day.  Thus  from  Oct.  31  to  Nov.  30  is  a 
calendar  month. 

From  Aug.  20,  1854,  to  March  10,  1857,  would  be, 
according  to  the  1st  Rule,  2  yrs.  6  mo.  20  d. ; 
"          "        2d  Rule,  2  yrs.  6  mo.  18  d. 

From  Aug.  31,  1854,  to  March  10,  1857,  would  be, 
according  to  the  1st  Rule,  2  yrs.  6  mo.  9  d. 
•<          "        2d  Rule,  2  yrs.  6  mo.  10  d. 

It  will  be  observed  that  in  these  particular  examples,  though 
the  actual  difference  of  time  in  the  two  cases  is  11  days,  the 
result  by  the  second  rule  shows  only  8  days.  A  discrepancy  of 
2  days  may  also  arise  in  the  use  of  the  first  rule,  for  by  it  the 
time  from  Feb.  28,  1857,  to  March  2,  1857,  would  be  4  days, 
while  the  actual  time  is  only  2  days.  The  first  rule  also  shows 
no  difference  of  time  between  March  31  and  April  1.  Each  rule 
will  give  a  result  sometimes  too  large  and  sometimes  too  small. 

The  examples  in  this  work,  except  those  in  Bank  Discount, 
and  those  otherwise  restricted,  may  be  wrought  by  the  second 
rule. 

ART.  97.  PROBLEMS  IN  WHICH  THE  INTEREST  is  KNOWN. — 
Of  the  four  quantities,  the  principal,  time,  rate  per  cent.,  and 
interest,  to  find  either  one  of  the  first  three,  the  remaining 
three  being  given,  we  have  the  following 


126  INTEREST. 

G- E  ]ST  E  R  A  IL,     R-TILE. 

Find  the  interest  by  the  given  conditions,  assuming  one 
dollar  for  the  principal,  one  per  cent,  for  the  rate,  or  one  year 
for  the  time,  in  place  of  the  unknown  quantity,  as  the  case  may 
be,  by  which  divide  the  given  interest,  and  multiply  the  assumed 
amount  by  the  quotient. 

Unity  is  assumed  for  convenience  only  in  multiplication. 

Note. — When  the  amount  is  given  instead  of  the  interest, 
to  find  the  latter  subtract  the  principal  from  the  amount. 

E  x  am.  pies. 

1.  What  is  the  rate  of  interest  if  I  receive  $20.96  for  the 
use  of  $126.75  for  2  yrs.  24  d.  ? 

Solution. — At  \%  I  would  have  received  $2.62,  and  since 
the  given  interest  is  eight  times  this,  the  rate  should  be  eight 
times  \%. 

2.  What  sum  invested  at  10$  per  annum  will  secure  an 
income  of  $1000  semi-annually  ? 

Solution. — One  dollar  thus  invested  would  yield  an  income 
of  5  cents  semi-annually,  and  since  $1000  is  20,000  times  5 
cents,  the  sum  loaned  should  be  20,000  times  one  dollar. 

3.  In  what  time  will  $512.60  amount  to  $538.31  at  1% 
per  annum  ? 

Solution. — The  interest  of  $512.60  in  one  year  would  amount 
to  $35.88,  and  since  the  given  interest  is  only  $25.71,  the  re- 
quired time  would  be  ff:fj  of  1  year,  which  by  reduction  will 
be  found  to  be  8  mo.  18  d. 

Fractional  days  in  the  result  may  of  course  be  neglected. 

ART.  98.  The  same  result  may  be  obtained  by  making  the 
statement  in  the  form  of  a  proportion,  though  it  is  better  to 
work  by  analysis. 

The  above  examples  would  be  thus  stated  : 

As  $2.62  int.  at  \%  is  to  $20.96  given  int.,  so  is  \%  the 
supposed  rate  to  8%  the  required  rate. 

Or,  $2.62  :  $20.96  :  :  \%  :  8$. 

2.  $0.05  :  $1000  :  :  $1  :  $20,000. 

3.  $35.88  :  $25.71  :  :  1  yr.  :  8  mo.  18  d. 


INTEREST.  127 

4.  In  what  time  will  any  sum  double  itself  by  simple  in- 
terest at  5  per  cent.  ? 

Solution. — The  required  interest  must  be  100$  of  the  prin- 
cipal, and  as  there  is  a  gain  of  only  5$  in  one  year,  it  will  take 
as  many  years  as  5  is  contained  times  in  100. 

Note. — To  treble  itself,  the  required  interest  must  be  200$ 
of  the  principal. 


PRESENT     -WORTH. 

ART.  99.  Simple  interest  varies  directly  as  the  principal, 
time,  and  rate  per  cent.  Either  two  of  'the  latter  terms  re- 
maining the  same,  interest  varies  as  the  other.  The  principal 
being  given  or  fixed,  the  amount,  consisting  of  the  sum  of 
principal  and  interest,  or  of  a  constant  and  variable  quantity, 
can  not  vary  as  the  time  and  rate  per  cent.  But  if  the  time 
and  rate  per  cent,  are  constant  quantities,  the  interest  varies  as 
the  principal,  and  the  amount  being  in  this  case  the  sum  of 
two  equally  varying  quantities,  varies  also  as  the  principal. 
From  this  we  see  the  truth  of  the  following 

PROPOSITION. — For  the  same  time  and  rate  per  cent.,  whether 
the  interest  be  -simple  or  compound,  the  amount  due  varies  as 
the  principal. 

The  Present  Worth  of  any  debt  is  the  sum  or  principal 
which  at  the  current  rate  of  interest  will  amount  to  that  debt 
when  it  becomes  due. 

For  example,  $100  at  10$  will  amount  in  one  year  to 
§110.  The  Present  Worth  then  of  $110  due  one  year  hence  is 
$100. 

The  amount,  rate,  and  time  being  given,  to  find  the  prin- 
cipal or  Present  Worth,  we  have  the  following 

RTJLE. 

Assuming  any  principal,  determine  the  amount  for  the 
given  rate  and  time,  by  which  divide  the  given  amount,  and 
multiply  the  assumed  principal  by  the  quotient. 


128  INTEREST. 

Note. — To  render  the  multiplication  easy,  assume  $1  or 
$100. 

Remark. — The  difference  between  the  Present  Worth  and 
the  Amount  of  the  debt  is  called  the  Discount ;  and  is  really 
the  interest  on  the  Present  Worth.  For  Bank  Discount,  see 
Art. 

Examples. 

1.  What  is  the  present  worth  and  discount  of  a  debt  of 
$1000  due  in  1  yr.  6  mo.,  the  current  rate  of  interest  being  6 
per  cent.  ?        Ans.  Pres.  Worth,  $917.431 ;  Dis.,  $82.569. 

2.  What  sum  must  I  put  at  interest  at  10  per  cent,  to 
liquidate  a  debt  of  $3000  due  3  years  hence  ? 

3.  A  man  can  sell  his  farm  for  $5000  cash,  or  for  $6000 
payable  in  2  years  ;  if  he  accept  the  last  offer,  and  receive  in- 
stead its  present  worth  at  8%  interest,  how  much  better  would 
it  be  than  the  first  offer  ?     If  he  accept  the  first  offer,  and  loan 
the  $5000  at  8%  interest,  how  much  less  would  he  receive  at 
the  end  of  the  2  years  than  if  he  accept  the  last  ?     What  is 
the  present  worth  of  that  difference  ? 


ANNUAL     INTEREST. 

ART.  100.  If  a  note  reads  "  with  interest  payable  an- 
nually," or  "  with  annual  interest/'  the  interest  may  be  col- 
lected at  the  close  of  each  year  ;  but,  if  not  paid,  the  interest 
due  draws  only  simple  interest  to  the  time  of  maturity,  or  until 
paid. 

It  is  a  principle  in  law,  that  money  due  or  on  interest  al- 
ways draws  simple  interest,  unless  a  condition  to  the  contrary 
is  expressly  stated.  The  condition,  "with  interest  payable 
annually,  applies  to.  the  interest  which  accrues  on  the  princi- 
pal or  face  of  the  note,  and  not  to  the  interest  on  the  annual 
interest. 


INTEREST.  129 

If,  when  the  annual  interest  is  not  paid  at  the  close  of  each 
year,  separate  notes  for  the  same,  drawing  simple  interest, 
should  be  given,  the  sum  of  the  amounts  due  on  the  several 
notes,  including  the  original,  would  be  the  same  as  the  amount 
due  on  the  one  note  with  annual  interest  unpaid  till  the  time 
of  maturity  or  settlement. 

Ex.  1. 

$500.  CLEVELAND,  May  10,  1850. 

For  value  received.  I  promise  to  pay  John  Smith,  or  bearer, 
five  hundred  dollars,  four  years  from  date,  with  interest  at  10 
per  cent.,  payable  annually. 

JAMES  HOLT. 

Nothing  being  'paid  till  time  of  maturity,  what  will  be  the 
amount  then  due  ? 

Operation. 

Principal, $500 

Interest  on  the  principal  1  vr.      =$50 

4yrs.    =  8200 

Simple  interest  on  $50  for  3  yrs.=$15 
"  "  2yrs.=    10 

"  "  JL  yr.  =    _5 

6yrs.=    '  30 

Total  amount  due  at  maturity,    .         .     $730 

Explanation. — At  the  close  of  the  1st  year,  $50  annual  in- 
terest was  due,  but,  being  unpaid,  draws  simple  interest  to  the 
time  of  maturity,  or  3  years  ;  at  the  close  of  the  2d  year,  $50 
annual  interest  was  again  due,  which,  being  unpaid,  draws 
simple  interest  2  years  ;  at  the  close  of  the  3d  year,  $50  annual 
interest  is  again  due,  and  draws  simple  interest  1  year ;  at  the 
close  of  the  4th  year,  or  time  of  maturity,  §50  is  again  due, 
but,  being  paid,  has  no  interest.  Hence,  the  total  interest  due 
consists  :  1.  Of  the  annual  interest  (§50)  multiplied  by  4,  the 
number  of  years  to  maturity.  2.  Of  the  simple  interest  of  the 
annual  interest  (§50)  for  3  years,  for  2  years,  for  1  year,  or  for 
3^2  +  1  years— 6  years. 

Note. — It  will  be  noticed  that  the  amount  due  consists  cf 
three  parts  :  1.  Principal.  2.  Total  annual  interest.  3.  Simple 
interest  on  annual  interest. 


130  INTEREST. 

Ex.  2. 

$1000.  BUFFALO,  Jan.  1,  1853. 

For  value  received,  I  promise  to  pay  Thos.  Hunt,  or  order, 
May  7,  1858,  one  thousand  dollars,  with  annual  interest  at  G 
per  cent.  G-EO.  SWIFT. 

Nothing  heing  paid  on  the  above  note  till  time  of  maturity, 
what  will  be  the  amount  then  due  ? 

Operation. 
Principal,        .         .         ......     $1000 

Interest  on  the  prin.  1  yr.,  or  annual  interest,  —  $60 
"  "      *  5  yrs.  4  mo.  6  da.,  the  entire 

time  of  the  note  computed  as  in  simple  int.—         321 
Simple  interest  on  $60  for  4  yrs.  4  mo.-  6  d. 

((  a  3     a     4     u     6  " 

K  a  2    a   4    u    6  u 

ic  a  1     "    4     "     6  " 

cc  tc  4    "    6  " 


Total  amount  due  at  maturity,  .  .  .  $1363.30 
Note.  —  In  this  case,  the  amount  due  consists  of  three  parts 
as  in  Ex.  1.  The  term  "  total  annual  interest"  as  used  above, 
though  nothing  more  than  the  simple  interest  on  the  principal, 
signifies  that  debt  of  interest  which  if  not  paid  draws  interest. 
As  all  interest  is  due  at  settlement,  that  which  has  accrued  at 
the  time  of  settlement,  though  for  less  than  a  year,  as  in  the 
last  example,  may  still  be  classed  with  "  annual  interest/' 


Find  the  simple  interest  on  the  principal  for  the  entire  time, 
which  will  be  the  TOTAL  annual  interest. 

Then  find  the  SIMPLE  interest  on  the  annual  interest  for  one 
year,  for  a  time  equal  to  the  SUM  of  the  periods  of  time  the 
several  annual  interests  draw  interest. 

The  sum"  of  the  principal,  total  annual  interest,  and  simple- 
inter  est  thus  found,  will  be  the  amount  due  at  maturity.  Or, 

On  the  annual  interest  due  each  year,  compute  SIMPLE  IN- 
TEREST till  maturity,  and  to  the  sum  of  their  several  amounts 
add  the  principal. 

When  the  interest  is  payable  semi-annually  or  quarterly, 


INTEREST.  131 

each  semi-annual  or  quarterly  interest  draws  simple  interest 
till  paid. 

IE  x  a,  m.  pies. 

3.  A  note  for  $1200  is  given' to  run  3  yrs.  3  mo.  12  d.  with 
interest  at  6  per  cent.,  payable  annually.     Nothing  being  paid 
till  maturity,  what  is  then  due  ?  Ans.  $1453.03. 

4.  Bought  a  city  lot  for  $900,  to  be  paid  in  4  equal  annual 
payments  with  annual  interest.     Nothing  being  paid,  what  is 
due  5  years  from  the  date  of  the  article  or  lease  ?     What,  4 
yrs.  7.  mo.   9  d.  ?      What,   10  years,  interest  payable  semi- 
annually  ?  Ans.  to  the  last,  $1593.90. 

5. 

§2000.  CLEVELAND,  March  15,  1853. 

On  the  first  day  of  January  1858,  for  value  received,  I 
promise  to  pay  John  F.  Whitelaw,  or  order,  two  thousand 
dollars  with  annual  ^interest.  CHARLES  L.  CAMP. 

WThat  was  due  at  maturity,  no  interest  having  been  paid  ? 
What  was  due,  supposing  the  annual  interest  to  have  been 
paid  promptly  ? 


COMPOUND     INTEREST. 

ART.  101.  In  Compound  Interest,  as  before  stated,  the 
entire  amount  due  at  regular  intervals  of  time,  whether  prin- 
cipal or  interest,  is  converted  into  one  new  principal.  It  may  be 
thus  compounded  annually,  semi-annually,  or  quarterly. 

For  illustration,  consider  $1  to  draw  interest  at  6%  and 
compounded  annuallv. 

$1. 

1st  year's  interest,       ....  .06  • 

Amount  due  forming  a  new  principal,  1.06 

2d  year's  interest,        .  .0636 

Amount  due  forming  a  new  principal,  1.1236 

3d  year's  interest, 067416 

Amount  due  forming  a  new  principal,  1.191016 

4th  year's  interest, _.07146096 

Amount  due  in  four  years,           .         .  $1^26247696 


132 


INTEREST. 


Amount  of  $1  at  Compound  Interest  in  any  number  of  years. 


Yrs. 

2  per  cent. 

2^  per  cent. 

8  per  cent. 

oi  per  cent. 

4  per  cent. 

4£  per  cent 

1 
2 
3 
4 
5 

1.0200  0000 
1.0404  OoiiO 
1.0612  0300 
1.0824  3216 
1.1040  8080 

1.0250  0000 
1.0506  2500 
1.0763  9062 
1.1038  1289 
1.1314  0821 

1.0300  0000 
1.0609  0000 
1.0927  2700 
1.1255  0881 
1.1592  7407 

l.t.350  0000 
1.0712  2500 
1.1087  1787 
1.1475  2300 
1.1876  8631 

1.0400  0000 
1.0816  0000 
1.1248  6400 
1.1698  5856 
1.2166  5290 

1.0450  0000 
1.0920  2500  ! 
1.1411  6612  1 
1.1925  I860 
1.2461  8194 

6 

7 
8 
9 
10 

1.1261  6242 
1.1436  8567 
1  1716  5938 
1.1950  9257 
1.2189  9442 

1.1596  9342 
1.1886  8575 
1.2184  0290 
1.2488  6297 
1.2800  8454 

1.1940  5230 

1.2298  7387 
1.2607  7008 
1.3047  7318 
1.3439  1638 

1.2292  5533 
1.2722  7926 
1.3168  0904 
1.3628  9735 
1.4105  9376 

1.2653  1902 
1.3159  3173 
1.8685  6905 
1.4288  11  SI 

1.4802  4423 

1.3022  6012 

1.3ft.  8  6183 
1.4221  0061 
1.4860  9514 
1.5529  0942 

11 
12 
13 
14 
15 

1.2433.  7431 
1.26S2  4179 
1.2938  0663 
1.3194  7876 
1.3458  6834 

1.3120  8666 
1.8443  8SS2 
1.3785  1104 
1.4129  7382 
1.4482  9317 

1.3842  3387 
1.4257  6039 
1.4685  3371 
1.5125  8972 
1.5579  6742 

1.4599  6972 
1.5110  6866 
1.5689  5606 
1.6186  9452 
1.6753  4883 

1.5394  5406 
1.6010  3222 
1.6650  7351 
1.7316  7645 
1.8009  4351 

1.6228  5305 
1.6958  8143 
1.7721  9610 
1.8519  4492 
1.9352  8-44 

16 
17 
IS 
19 

20 

1.8727  8570 
1.4002  4142 
1.42.32  40  J5 
1.4563  1117 
1.4859  4740 

1  4845  0562 
1.5.'  10  1826 
1.5596  5872 
1.5986  5019 
1.6386  1644 

1.6047  0644 
1.6528  4763 
1.7  24  3306 
1.75-35  0605 
1.8061  1123 

1.7339  8601 
1.7946  7555 
1.8574  8920 
1.9225  0132 
1.9897  8386 

1.8729  8125 
1.9479  0050 
2.0253  1652 
2.10G8  4918 
2.1911  2314 

2.0223  7015 
2.1188  7681 

2.2084  7s77 
2.3u78  6031 
2.4117  14U2 

21 

22 
23 
24 
25 

1.5156  6634 
1.5459  7967 
1.5768  9926 
1.6  )84  8725 
1.6406  0599 

1.6795  8185 
1.7215  7140 
1.7646  1068 
1.80S7  2595 
1.8539  4410 

1.8602  9457 
1.9161  0341 
1.9735  8651 
2.0327  9411 
2.0937  7793 

2.0594  8147 
2.1315  1158 
22061  1448 
2.2333  2349 
2.3G32  4498 

2.27S7  6S07 
2.3699  1^,79 
2.4647  155  1 
2.5683  0417 
2.6658  8633 

2.5202  4116 
2.6336  52  il 
2.7521  6635 
2.&760  1383 
3.01,54  8446 

26 

27 
28 
29 
30 

1.6734  1811 
1.7068  8648 
1.7410  2421 
1.7753  4169 
1.8113  6158 

1.9002  9270 
1.9478  0002 
1.9964  9502 
2.0464  0739 
2.0975  6753 

2.1565  9127 

2.2212  89',  1 
2  2379  2768 
2  3565  6551 
2.4272  6247 

2.4459  5356 
2.5315  6711 
2.6201  7196 
2.7118  7798 
2.8067  9370 

2.7724  6979 

2.8333  6358 
2.9937  0332 
3  1186  5145 
3.2433  9751 

3.1406  7901 
3.2320  0956 
3.4296  9999 
3.5340  3649 
3.7453  1813 

31 
•32 
33 
84 
35 

1.8475  8882 
1.8345  4059 
1.9222  8140 
1  9606  7603 
1.9998  8955 

2.1500  0677 
2.2037  5694 
2.2583  5086 
2.3153  2213 
2.3732  0519 

2.5000  8035 
2.5750  8276 
2.6523  3524 
2,7319  0530 
2.8138  6245 

2.9050  3148 
8.0067  0759 
3.1119  4235 
3.2208  6033 
3.3335  9045 

8.3731  3341 
8.5080  5875 
3.6483  8110 
3.7943  1634 
3.9460  8899 

8.9138  5745 
4.0899  8104 
4.2740  3018 
4.4663  6154 
4.6673  4781 

36 
37 
33 
39 
40 

2.0393  8734 
2.0306  8509 
2.1222  9379 
2.1G47  4477 
2.2080  3966 

2.4325  3532 
2.4933  4370 
2.5556  8242 
2.6195  7448 
2.6850  6384 

2,8932  7833 
2.9*52  2668 
3.0747  8348 
3.1670  2693 
3.2620  8779 

3.4502  6611 
3.5710  2543 
3.6960  1132 
3.3253  7171 
3.9592  5972 

4.1039  3255 

4.2630  8986 
4.4388  1345 
4.6163  6599 
4.8010  2063 

4.8773  7846 
5.G9G8  6049 
5.8/62  1921 
5  5658  9908 
5.8163  6454 

41 
42 
43 
44 
45 

2.2522  0046 
2  2972  4447 
2.3431  8936 
2.890i  >  5314 
2.4378  5421 

2.7521  9043 
2.821)9  9520 
2.S915  2008 
2.9638  0803 
3.0379  0328 

3.3598  0-93 
34606  9>S9 
3  5645  1  )77 
3.6714  5227 
8.7&15  95s4 

4.0978  8381 
4.2412  5799 
4.3897  0202 
4.5433  4160 
4.7023  5855 

4.9930  C145 
5.1927  8391 
5.4004  9527 
5.6165  1503 
5.8411  7568 

6.0781  0094 
6.3516  1543 
6.6374  SS18 
6.93(11  2-_>!m 
7.2482  4843 

46 
47 

49 
50 

'2.4366  112!) 
2.5363  4351 
2.5s7i)  703!) 
2  'I'!--;  117!) 
2.6915  8803 

3.1133  5086 
8.1916  9713 
3.2714  8956 
8.3532  7630 
3.4371  0872 

3.8950  4372 
4.0118  9503 
4.1322  5183 
4.25IV2  ]!>U 
4..-3S30  0602 

4.8669  4110 

5o:;72  8404 
5.2135  8S98 
5.3960  <;!.v,» 
5.5849  2636 

6.0743  2271 

6.3178  1562 
«.57«'5  2824 
6.8333  4937 
7.1066 

7.5744  1961 
7.9152  G849 
8.2714  f.557 
f.<54«(5  7107 
9.0326  3627 

51 

2.7454  1!»7'' 

-V;2°>0  •%  U 

4..MT4  '_'-;•-"> 

;  99!10 

7  ."/)"'.)  r>i!G3 

9.IS91  049) 

53 
54 
55 

:  8475 

2<n:!t  um 

2.9717  3067 

:',  7  1  >>  !>iiK> 
3.7939  2«91 
,  7808 

-!  7!)  4  1247 
4.  9341  2435 
:>.oxU  4359 

(1  '921  0824 
640SS  3202 
6.6331  4114 

7.9910  :.22i; 
s.;i!:;s  1  |:i;, 
8.6463  6G92 

10  3o77  8858 
10.7715  8(577 
11.2563  OS17 

INTEREST. 


133 


Amount  of  §1  at  Compound  Int€rest  in  any  number  of  years. 


r» 

1 
2 
3 
4 

5 

5  per  cent. 

6  per  cent 

7  per  cent. 

8  per  cent 

9  per  cent        10  per  cent 

l.tlSftO  000 
1.1  '.' 
1.153 
1.2;: 
1.27 

1.0600  000 
1  1-236  000 
1.1910  160 
1.2624  770 
1.....352  256 

1.0700  000 
1  1449  000 
l.-.'^oO  430 
1.3107  960 
1.4025  517 

1.0800  000 
1.1664  000 
12597  120 
1.3604  890 
1.4693  231 

1.0900  OCO 

i.:>-i  (MM) 

1.2950  290 
1.4115  816 
1.5i>86  240 

1.1  COO  000 
1  2100  COO 
1.3310  000 
1.4641  000 
1.01(5  100 

6 

T 
8 
9 
10 

1.3400  95<i 

1.4071  o-4 
1.4774  S:,4 
1.5-  : 
L628S  946 

1.4185  191 
1.5036  8(i3 

1.593-  4-1 
-  4  790 
1.790S  477 

1.5007  304 
1.6057  815 
1.71S1  862 
1.-3S4  592 
1.9671  514 

1.5863  743 
L7133  243 
1.5509  3(12 
1.9990  046 
2.1589  250 

1.6771  001 
1.8280  S91 
1.9925  626 
2.1718  983 
2.3673  637 

1.7715  610 
1.94S7  171 
2.1485  888 
2.8579  477 
2.5937  425 

11 
12 
13 
14 
15 

1.7103  394 
1.7953  5t>3 
•  •»  491 
1.9799  316 
1  -J  232 

1.8P- 
•2.0121  965 
2.1329  2S3 
0  040 
2.35 

2.1043  520 
2.2521  916 
2.4<>93  450 
2.5785  342 
2.7590  315 

23316  390 
2.51S1  7ol 
2.7196  237 
2.9371  936 
3.1721  691 

2.5804  264 

-6  64S 
3.o»'.:  - 
3.3417  270 
aC424  S25 

2  8c31  167 
3.1:  - 
8.4522  712 
3.71-74  9S3 

4.177. 

16 
17 

13 
19 
20 

B8  746 

2.2920  1S3 
24066  192 
2.5269  502 
2.6532  977 

2.54C3  517 
2.6927  7-2- 
2.S543  392 
156  905 
3.2071  S55 

2.9521  633 
3  1533  152 
3.3799  323 
3.6165  275 
3.8696845 

3.4259  426 
3.7000  181 
3.9960  195 
43157  01  1 
46609  571 

3.9703  059 

43270  834 
4.7171  204 
5.1416  613 

5.6044  1  3 

45949  730 

5J/44  7d3 
5.5599  173 
6.  1  1.'9  S90 
6.7275  000 

21 

24 
25 

£B  626 

2.92  - 
3.0715  233 
3.2250  999 
3.3S63  54 

3.3995  636 
3.6035  374 
7  497 
4.0459  346 
4.2&1 

4.1405  624 
4.4304  017 
4.7405  299 
5.0723  670 
5.4274  326 

5.0333  837 
5.43G5  4i  4 
5.S714  637 
6.3411  -<7 
6.34S4  752 

6.1'- 

6.6566  -".4 
7.2^7 
7.9110  852 
8.6230  807 

7.401-2  499 
8.1402  749 
8  (24 
9.5497  3-7 
10.8347  059 

26 
2T 
28 
29 
M 

3.5556  727 
3.7334  563 
3.9201  291 
4.1161.  356 
4.3219  424 

4.5493  830 

-_. 
5.1116  867 
5.41S3  S79 
5.7434  912 

5.8073  529 
6.21: 

6.G4S3  384 
7.1142  571 
7.6122  550 

7.3963  532 
7.9SSO  610 
7!  064 
9.3172  749 
10.0626  5C9 

9.3991  579 

10.24: 
11.1671  :-05 
12.1721  821 
13.2670  7;5 

11.9181  765 
13.1099  942 
14.42(9  936 
15.-f3o  930 
17.4494  023 

31 
89 

33 

34 
35 

4.53^  395 
4.7649  415 
5.0031   385 

5.2.-:  -> 
5.5160  154 

6.r.881  006 
6.454 

•1-405  899 
72510  25=3 
7.6360  8C8 

8.1451  129 
8.7.:.. 
9.3253  398 
rSl   135 
10.6765  815 

10.8676  694 
11.  7370  S30 
12.6760  4!»0 
18.6901  336 
14.7853  443 

144617  695 

15.703:;  i-3 
l7.1S-_"'  -'-4 
IS  72S4  109 
20.4139  679 

19.1943  425 
21.1137  768 
:i  544 
25.5476  C99 
2J-.1024  S69 

36 

87 
33 
39 
40 

5.7913  161 
6.0-  ;  ; 
6.8354  773 
6.70  '  ' 

7.031*. 

S.I  472  520 
10  S71 
9.1542  524 
9.70- 
10.2857  179 

11  4239  422 
12.2236  1-1 

13."7'.'2  714 

13.9:>  g 

14.9744  573 

15.9681  718 
17.2-156  256 
IS  6252  7:0 
20.1152  !•" 
21.7245  215 

22.2:  1 

26.4::,- 
2e.S159  817 
31.4<;94  200 

30.9126  805 
S4.U 
43  434 
4114-.1  77- 
45.'25t2  656 

41 
42 
43 
44 
45 

7.391. 
7.761: 
8.1496  669 
8.5571  5'3 
8.9850  078 

10.9023  610 
11.557 
122.-i.i4  546 
12.9S54  -10 
13.7t>4a  11..  s 

1C,.  ir2-26  699 
17.1442  563 
is  34  13  543 
19.62>4  596 
21.0024  513 

23  4624  832 
25.3394  £19 
27.8660 

29.5559  717 
31.9204  494 

34.2362  679 
37.317 
40.67 
448» 
48.3272  601 

49.7851  811 
86  9t.2 
60.24 

C6.2640  761 
72.8904  637 

46 

47 

49 

50 

9.4342  582 
9.9  >59  711 
1  ..4012  697 
1  ».9-213  831 
11.4673  993 

14.5904  -75 
15.4659  1>  7 
16.3933  717 
17.3775  H40 
18.4201  543 

•22  -1726  234 
•J4."4.-7  i7-i 
•2:.  72-9  065 
.'  800 
29.4570  251 

S44740  853 
20  122 

4-  i-.'li  5  7S1 
4-U.74  I9i» 
46.9016  1-5 

52.6767  419 

57.417 
6_'5-- 
Cs-2179  OS3 
74.3575  2'1 

80.1795  ?21 
88.1974  853 
'.•-  0172*888 
'106.7189  572 
117.3908  529 

51 
53 
53 
54 
55 

1-2.0407  693 
12.6423  083 
13-2749  4b7 
13.93-6  961 
146356  809 

19.52.V 
20.69-N 
21.9386  985 
23.2550  204 
246503  216 

81.5190  163 
58  450 
M   224 
-1  509 
41.3150  015 

50.6537  415 
54.T06I 

5  -241 
63.8091  260 
68.9133  561 

SI  .0496  9<-f> 

96.2951   -449 
1  1"4.961  7  079 
114.4(82  616 

129.1299  382 
142.042! 

156.  '2-1  72  252 
'  '  '.'  477 
1S9.I.591  425 

134  INTEREST. 

If  compounded  semi-annually,  we  should  have  the  follow- 
ing result  : 

$1. 

Interest  1st  six  months,  •    .         .         .         .03 

L03 

Interest  2d  six  months,       .         .         .         .0309 

1,0609 
Interest  3d  six  months,       .         .        .         .031827 

1.092727 

Interest  4th  six  months,      .         .         .         .03278181 

Amount  in  two  years,         .         .        .     $1.12550881 
We  have  seen  heretofore  that  simple  interest  varies  directly 
in  the  same  ratio  as  the  principal,  time,  and  rate  per  cent. 
Compound  interest  likewise  varies  as  the  principal,  but  when 
the  time  or  rate  per  cent,  is  increased,  compound  interest  in- 
creases in  a  still  greater  ratio,     e.  g. 
Doubling  the  principal  doubles  the  compound  interest. 
Doubling  the  time  more  than  doubles  the  compound  interest. 
Doubling  the  rate  more  than  doubles  the  compound  interest, 
as  may  be  seen  from  the  following  figures  : 
When  the  interest  of  $100  is          ....       $5. 
The  interest  of  $200  would  be       ...     $10. 

The  compound  interest  of  $100  for  2  years  at    6%  is  $12.36 
«  "  "         "      "      "  4  years  at    6%  is  $26.2477 

"  "         "      "      "  2  years  at    5%  is  $10.25 

1    «  "  "         "      "      "  2  years  at  10/0  is  $21. 

From  the  fact  that  compound  interest  (and  therefore  the 
compound  amount)  varies  as  the  principal,  the  time  and  rate 
remaining  the  same,  having  ascertained  the  interest  or  amount 
for  any  one  principal,  the  interest  for  any  other  may  be  found 
by  a  simple  proportion.  Tables  have  therefore  been  prepared 
giving  the  interest  or  amount  of  $1  for  different  intervals  of 
time  and  at  different  rates  per  cent.  The  interest  or  amount 
for  any  given  principal  may  then  be  found  by  simply  multiply- 
ing the  sum  found  in  the  table  by  the  given  principal.  If  the 
intervals  are  less  than  one  year,  as  when  the  interest  is  to  be 
compounded  semi-annually  or  quarterly,  tables  computed  with 
yearly  intervals  may  still  be  used  by  reducing  the  rate  per  cent. 


INTEREST.  135 

proportionably,  and  taking  in  the  table  the  proper  number  of 
intervals. 

For  the  time  used  in  expressing  any  rate  of  interest  is  en- 
tirely arbitrary,  and  having .  fixed  the  ratio  between  the  prin- 
cipal and  interest  at  each  compounding,  the  result  depends 
upon  the  number  of  times  the  operation  be  repeated.  Thus, 
if  the  interest  be  compounded  a  given  number  of  times  by  add- 
ing to  each  respective  amount  4$  of  itself,  it  matters  not 
whether  it  be  considered  4$  per  annum  or  4^  per  minute,  the 
result  would  be  the  same.  If  the  interest  is  to  be  compounded 
quarterly,  when  the  rate  is  said  to  be  8^  per  annum,  2^ 
should  be  used  at  each  compounding,  though  it  would  amount 
to  more  than  8$  compounded  annually. 

Examples. 

1.  What  is  the  compound  interest  and  amount  of  $1000 
for  5  yrs.  at  Q%  per  annum,  payable  annually  ? 

"  Ans.  $338.22  and  $1338.22. 

2.  What  is  the  compound  amount  of  $2200  for  3  yrs.  2  mo. 
12  d.  at  6/p  per  annum,  payable  annually  ? 

Ans.  $2651.67. 

Note. — After  having  computed  the  compound  amount  for 
the  number  of  entire  intervals  at  the  end  of  which  the  interest 
is  payable  or  to  be  computed,  compute  the  simple  interest  on 
that  amount  for  any  remaining  time  before  the  settlement. 

3.  What  is  the  compound  interest  of  $1400  for  10  yrs.  8 
mo.  at  8/£  per  annum,  payable  quarterly. 

Solution.— $2.29724447  x  1400  =  $3216.1423  =  the  comp. 
amount  for  10  yrs.  6  mo.,  and  $3216.1423  x  l.Oli— $1400= 
the  comp.  interest  for  10  yrs.  8  mo. =$1859.024. 

4.  If  the  population  of  a  city  containing  10,000  inhabitants 
should  increase  10^  annually,  what  would  it  amount  to  in  10 
years?  Ans.  25,937. 

5.  If  a  farmer  beginning  with  one  bushel  of  wheat  should 
sow  his  entire  crop  each  successive  year,  and  the  increase  each 
year  should  be  1900^,  what  would  he  have  at  the  end  of  5 
years?  Ans.  3,200,000  bushels. 


136  INTEREST. 

6.  If  a  banker's  rate  in  loaning  money  is  12$  per  annum, 
and  lie  reloans  all  his  capital  every  two  months,  what  must 
have  been  the  rate  at  simple  interest  to  realize  the  same  amount 
at  the  end  of  one  year  ?  Ans.  12^$  nearly. 

What,  at  the  end  of  two  years  ?  Ans.  13T4¥$  nearly. 

What,  at  the  end  of  eight  years  ?  Ans.  19T3¥/^  nearly. 

What,  at  the  end  of  fifteen  years  ?  Ans.  33$  nearly. 

What,  at  the  end  of  twenty-five  years  ?       Ans.  74$  nearly. 

ART.  102.  In  compound  interest,  as  in  simple  interest,  the 
four  quantities,  viz.,  principal,  time,  rate  per  cent.,  and  interest 
or  amount,  bear  such  a  relation  to  each  other  as  that  when 
any  three  of  them  are  given,  the  fourth  may  be  found.  Hence 
four  cases  arise. 


i. 

The  principal,  time,  and  rate  being  given,  to  find  the  com- 
pound interest  and  amount. 

This  case  has  already  been  presented,  but  the  rule  may  be 
expressed  in  a  more  concise  form. 

KULE.  —  Find  from  the  table  the  amount  of  $l/or  the  given 
number  of  entire  intervals,  or  times  of  compounding,  at  the 
proper  rate  for  each  interval,  and  multiply  it  by  the  given 
principal.  Taking  this  product  for  a  new  principal,  find  the 
amount  at  simple  interest  for  any  fractional  interval,  if  any, 
remaining  before  settlement.  This  will  be  the  compound 
amount,  and  the  compound  interest  may  be  found  by  subtract- 
ing from  it  the  given  principal. 


II  . 

The  compound  interest  or  amount,  the  time  and  rate  being 
given,  to  find  the  principal. 

RULE.  —  Assume  $1  for  the  principal  /  compute  for  the 
given  time  and  rate  its  compound  interest  or  compound  amount, 
by  which  divide  the  given  compound  interest  or  compound 
amount,  observing  always  to  divide  interest  by  interest  and 
amount  by  amount.  See  Art.  97. 

For  illustration  of  Present  Worth  see  Art.  99. 


INTEREST.  137 

E  x  a  rn.  pies. 

1.  What  sum,  in  17  yrs.,  at  6^,  payable  annually  at  com- 
pound interest,  will  amount  to  §1009.79  ?  Ans.  $375. 

2.  What  sum,  in  14  yrs.,  at  8,V',  payable  semi-annually  at 
compound  interest,  will  amount  to  §10,795.34  ?    Ans.  §3COO. 

3.  What  principal  will  yield  §3251.50  compound  interest 
in  6  yrs.  2  mo.  at  7$,  payable  semi-annually  ?    Ans.  §6150. 

4.  How  much  must  a  father,  at  the  birth  of  his  son,  set 
apart  for  his  benefit,  so  that  with  the  interest  at  7%,   com- 
pounded semi-annually,  it  may  amount  to  §10,000,  when  his 
son  shall  become  21  years  of  age  ?  Ans.  §2357  79>. 

5.  What   sum  at   10/t,    payable   quarterly,    will    produce 
§7197.22,  compound  interest,  in  3  yrs.  6  mo.  9  d.  ? 

Ans.  §17,280. 

6.  What  is  the  present  worth  of  §50,000,  due  50  yrs.  hence, 
at  9  per  cent.,  payable  annually  ?  Ans.  §672.43. 

How  much  greater  would  be  the  present  worth  at  simple 
interest  ? 

CA.SE     III. 

The  principal,  time,  and  interest  or  amount  being  given, 
to  find  the  rate.     See  Case  IV. 

C.A.SE     I^T. 

The  principal,  rate,  and  interest  or  amount  being  given,  to 
find  the  time. 

For  the  last  two  cases  we  have  the  following  general 
KULE. — Divide  the  given  amount  by  the  principal ;  the 
quotient  will  be  the  compound  amount  of  §1  at  the  given  rate 
for  the  required  time  or  for  the  given  time  at  the  required  rate. 
By  reference  to  the  table,  the  rate  heading  the  column  in  which 
this  quotient  is  found  opposite  the  given  time  or  number  of  in- 
tervals, ivill  be  the  required  rate;  and  the  number  in  the  left 
hand  column  opposite  the  quotient  under  the  given  rate  will  be 
the  required  time  or  number  of  intervals. 

E  x  a  m.  pies. 

1.  At  what  rate  will  §7200  yield  §12,665.02,  compound  in- 
terest in  15  yrs.  ?  Ans.  7  per  cent. 


138  INTEREST. 

2.  At  what  rates  will  any  sum  of  money  double  itself  by 
compound  interest  in  8,  10,  15  yrs.  payable  semi-annually  ? 

Ans.  4i$,  3$,  2i$,  respectively. 

3.  In  what  time  will  $5428  amount  to  $27157.31  at  5$, 
payable  annually  ?  Ans.  33  yrs. 

4.  In  what  time  will  any  sum  of  money  triple  itself  by 
compound  interest  at  4$,  7$,  8$,  10$,  payable  quarterly  ? 

7  yrs.,  4  yrs.,  3^  yrs.,  3  yrs.  nearly. 


PARTIAL     PAYMENTS. 

ART.  103.  When  partial  payments  are  made  on  mercantile 
accounts  which  are  past  due,  and  on  notes  running  only  for  a 
year  or  less,  it  is  customary  to  use  the 


RTJLE3. 

Compute  the  interest  on  the  whole  debt  or  obligation  from 
the  time  it  began  to  draw  interest,  and  on  each  payment  from 
the  time  it  was  made  until  the  time  of  settlement,  and  deduct 
the  amount  of  all  the  payments,  including  interest,  from  the 
amount  of  the  debt  and  interest. 

Note.  —  When  a  partial  payment  is  made  on  a  note  or  obli- 
gation before  it  is  due,  no  part  is  applied  to  the  discharge  of 
the  interest,  but  the  whole  is  used  to  reduce  the  principal  in 
accordance  with  the  above  rule. 

$800.  CLEVELAND,  Nov.  18,  1856. 

Ninety  days  after  date,  I  promise  to  pay  to  the  order  of 
William  Penn  six  hundred  dollars,  with  interest,  value  re- 
ceived. WALTER  JOHNSON. 

Indorsements.—  Nov.  30,  $100  ;  Dec.  10,  $250  ;  Dec.  20, 
$100  ;  Jan.  2,  $80. 

What  was  due  at  maturity  ? 

$600,  with  interest  for  93  days,  amounts  to  $G09.30 

$100,  "  "  «  81  "  "  "  $101.35 
$250,  "  «  "  71  "  "  "  25296 
$100,  "  "  "  61  "  "  «  101.02 
$80,  "  "  "  48  "  "  "  80.64 
Sum  of  payments,  with  their  interest,  $535.97 

Amount  due  at  maturity,  Feb.  19,  1857,  "$73^33 


INTEREST.  139 

The  same  result  can  be  obtained  more  easily  by  the  use  of 


the  following 


IRTJ  JL.E. 


Multiply  the  amount  due  at  first,  and  the  balance  of  the 
principal  due  after  deducting  each  payment,  by  the  number  of 
days  that  elapse  between  the  several  payments,  add  all  the  pro- 
ducts, and  divide  the  sum  by  6000.  The  quotient  will  be  the 
interest  at  6  per  cent. 

Taking  the  same  example  as  above. 

§600  multiplied  by  12=      ......       7200 

§500  "  10=      .....  .  5000 

§250          "          "  10=      ......       2500 

§150          "          "  13=      ......       1950 

§70  "          "  48=      ......      J3360 

Sum  =      ......     20010 

Which,  divided  by  6000,  gives  for  the  interest  due  .  §3.33 
This  added  to  the  balance  of  principal,  gives  .  .  §73.33 

When  the  principal  does  not  draw  interest,  the  last  rule 
can  not  be  used  without  some  modification. 

When  the  time  of  the  note  or  obligation  is  more  than  one 
year,  the  following  rule  has  been  adopted  by  the  courts  of 
most  of  the  States,  and  by  the  Supreme  Court  of  the  United 
States,  and  may  therefore  bo  called  the 


STATES 

ART.  104.  Apply  the  payment  in  the  first  place  to  the  dis- 
charge of  the  interest  then  due  ;  if  the  payment  exceeds  the  in- 
terest, the  surplus  goes  toward  discharging  the  principal,  and 
the  subsequent  interest  is  to  be  computed  on  the  balance  of 
principal  remaining  due. 

If  the  payment  be  less  than  the  interest,  the  surplus  of  in- 
terest must  not  be  taken  to  augment  the  principal  ;  but  interest 
continues  on  the  former  principal  until  the  period  when  the 
payments  taken  together  equal  or  exceed  the  interest  due,  and 
then  the  surplus  is  to  be  applied  toivard  discharging  the  princi- 
pal, and  interest  is  to  be  computed  on  the  balance  as  aforesaid. 

This  rule  requires  that  the  payment  should  in  all  cases  be 
applied  to  the  discharge  of  the  interest  first,  then  the  principal. 


140 


INTEREST. 


Ex.  1.  For  value  received,  I  promise  to  pay  to  the  order  of 
C.  D.  Stratton  $16*50  on  demand,  with  interest  at  7$. 

J.  0.  SNYDER. 

CLEVELAND,  0.,  May  20,  1856. 

Indorsements.— Sept.  1,  1856,  $25  ; -Oct.  14,  1856,  $150; 
Mar.  20,  1857,  $45  ;  July  5,  1857,  $300. 

What  was  the  amount  clue  Nov.  11,  1857  ? 
Solution. — Interest  on   $1650  from   May  20, 
1856,  to  Sept.  1,  1856,  3  mo.  12  d.,  at  7%  per 

annum, .         $32.725 

The  payment,  $25,  being  less  than  the  interest  then 
due,  neglecting  the  former  work,  find  the  interest 
on  $1650  from  May  20,  1856,  to  Oct.  14,  1856, 
4  mo.  24  d. 


46.20 
1650. 


Amount  due,  Oct.  14,  1856,          .... 
Sum  of  the  two  payments,  $25  and  $150,  to  be 

deducted, 

Balance  due  after  the  second  payment, 

Interest  on  $1521.20  from  Oct.  14, 1856,  to  March 

20,  1857  ($46.14),  being  more  than  the  payment 

made,  find  the  interest  on  $1521.20  from  Oct. 

14,  1856,  to  July  5,  1857,  8  mo.  21  d. 


Sum  of  the  payments,  $45  and 

Balance  due  July  5,  1857, 

Interest  on  $1253.401  from  July  5,  1857,  to  Nov. 

11,  1857,  4  mo.  6d., 

Balance  due  on  settlement,  Nov.  11,  1857,    . 


1696.20 

175. 
1521.20 


J77.201 
15987401 

345.^ 
1253:401 


30.708 

.     $1284.109 

Note. — Frequently  an  estimate  of  the  interest  may  be  made 
mentally  with  sufficient  accuracy  to  decide  whether  it  be  not 
more  than  the  payment,  whereby  some  labor  may  be  saved. 
2.  A  note  of  $1200  is  dated  June  10,   1854,  on  which, 
Aug.  16,  1855,  there  was  paid,  .     $100 

Dec.  28,  1855,      «      «      «  .        .       200 

June  2,  1856,       "       "       "  .  25 

Dec.  29,  1856,      "      "       "  .  25 

June  1,  1857,       "       "      "  .  25 

Oct.  28,  1857,      "      "      "  .  500 


INTEREST.  141 

What  is  the  amount  due  Dec.  10,  1857,  the  interest  being 
6    ?  Ans.  §551.347. 

3.  BUFFALO,  X.  Y.,  April  10,  1852. 

One  year  after  date,  I  promise  to  pay  to  the  order  of  James 
Johnson   one  thousand  dollars,  with  interest,  value  received. 

THEODORE  LELAND. 

Note. — The  legal  rate  of  interest  in  New  York  is  7$. 
On  the  note  were  the  following  indorsements  : 
Nov.  10,  1853,  rec'd  $  80.50          Jan.  10,  1855,  rec'd  §450.80 
5,  1854,       "       100.  Oct.  1,  1857,       "        500. 

remained  due  Jan.  1,  1858  ?  Ans.  §170.146. 

CHICAGO,  July  15,  1854. 


>T\vo  years  from  date,  for  value  received,  I  promise  to  pay 
the  order  of  Peter  Finney,  six  hundred  and  fifty  dollars, 
with  interest  at  10/£,  payable  annually.         SILAS  WARREX. 

\Mr.  Warren  paid  on  the  above  note,  Sept.  15,  1856,  §105  ; 
ay  9,  1857,  §250.     What  amount  was  due  Sept.  24,  1858  ? 

Note. — In  cases  like  the  last,  the  payments  should  be  ap- 
plied first  to  the  discharge  of  the  interest  on  the  annual  interest, 
then  the  annual  interest,  and  finally  the  principal.  The  in- 
terest on  the  principal,  which  has  not  yet  become  annual  in- 
terest, not  being  due,  should  not  be  cancelled  by  payments 
except  it  be  at  the  final  settlement  of  the  note. 

Solution. 

First  annual  interest, $65. 

Interest  on  same  from  July  15,  1855,  to  Sept.  15,  1856,       .  7.5SJ 

Second  annual  interest, C5. 

Interest  on  same  from  July  15,  1856,  to  Sept.  15,  1856,        .  1.0S3 

$138.66~6 

First  payment 105. 

Interest  on  $33.666  from  Sept.  15,  1856,  to  May  9,  1857,    . 
Original  principal,        ........ 


685.854 
Second  payment, 250. 

Xo\v  principal,  '.  $135.854 

Interest  on  $650  from  July  15,  1856,  to  May  9,  1857, 

not  due  at  time  of  payment,  •  $53.083 

Interest  on  $435.854  from  May  9,  to  July  15,       .  7.990 

Third  annual  interest,, 

Interest  on  same  from  July  15,  1857,  to  Sept.  24,  1858, 

Fourth  annual  interest, 

Interest  on  same  from  July  15.  1858,  to  Sept.  24,  1858, 

Fifth  annual  interest,  due  at  settlement, 

Amount  due  Sept.  24,  1858, 


ra|' 
in 


142  INTEREST. 

ART.  105.  Another  rule  for  applying  partial  payments  is 
in  use  among  many  business  men,  and  has  received  the  sanction 
of  several  legal  decisions.  This  rule,  because  it  is  used  by 
merchants,  has  been  styled 

THE     MEPtC^LlNrTIIjirj     RTJT^n. 

Compute  the  interest  on  the  principal  or  original  debt  for 
one  year,  and  add  it  to  the  principal.     Find  the  interest  also 
on  the  payments  made  during  the  year,  if  any,  from  the  time 
they  were  made  to  the.-  end  of  Ike  year.     Deduct  the  sum 
payments  and  interest  from  the  amount  of  principal  ami 
terest  for  a  new  principal.     Do  the  same  for  each  succeeding 
year  till  the  final  settlement. 

Note.  —  It  will  be  observed  that  this  is  applying  the 
mont  Rule  to  eaph  separate  year,  beginning  with  the  date 
the  note,  and  making  yearly  rests.     Sometimes  these  rests,  or 
times  of  making  a  new  principal  in  mercantile  accounts,  a 
made  to  come  at  the  end  of  each  civil  ^s-r,  sometimes  once  i 
six  months,  depending  upon  the  custom  of  merchants  in  balanc- 
ing their  accounts.      Bankers  for  the  same*reason  have  been 
allowed  to  make  quarterly  rests,  carrying  forward  a  new  prin- 
cipal every  quarter,  at  the  time  of  "balancing  the  ledger. 

Ex.  A  note  of  $2000  is  dated  Feb.  1,  1850,  on  which  were 
the  following 

Indorsements.  —  March  1,  1850,  $200  ;  July  1,  1850,  $300  • 
Oct.  1,  1850,  $500  ;  July  1,  1851,  $100  ;  Oct.  1,  1852,"  $200  ; 
Jan.  1,  1853,  $600. 

What  was  due  July  1,  1853,  the  interest  being  6;^  ? 
$2000  will  amount,  Feb.  1,  1851,  to         ...  $2120 
200     "         "  "      to         .  $211 

300     "  "•     to          .     310.50 

500     "         "  "         "      to         .     510 

Sum  of  payments  and  interest,          ....     1031.50 

New  principal,          .......     1088.50 

$1088.50  will  amount,  Feb.  1,  1852,  to     .  .     1153.81 

100         "          "  "         "     to     .         .         .       103.50 

New  principal,  .......     1050.31 

[Carried  over.] 


INTEREST.  143 

[Brought  over.] 

$1050.31  will  amount,  Feb.  1,  1853,  to     .  .     1113.33 

200          "  "  "         "     to     .  $204 

600.         "  "  "         "     to     .     603       .       807 

New  principal, 306.33 

$306.33  will  amount,  July  1,  1853,  to      ...       313.99 
ART.  106.  MERITS   OF   THE   BULKS   FOR   PARTIAL   PAY- 
MENTS.— The  method  of  computing  interest  when  partial  pay- 
ti&ents  have  been  made  is  a  subject  that  has  given  rise  to  much 
^itigation.     In  many  States  the  only  law  relating  to  it  consists 
•bf  decisions  in  particular  cas.es,  wliigk,  from  the  peculiar  cir- 
jcunwtances,  do  not  always  clearly  indicate  a  principle  that  may 
*  beiipplied  justly  to  other  cases.     The  aim  in  legislative  enact- 
ts  appears  to  have  been  twofold,  to  avoid  usury  and  the 
ing  of  compound  interest.      Now  all  interest  is  in  effect 
compounded  when  it  is  paid,  since  it  allows  the  lender  to  loan 
again  and  draw  interest  on  interest,  while,  if  not  paid,  the  debtor 
the  use  of  the  interest  money  without  paying  interest.     No 
court  ever  objected  to  a  man's  paying  interest  as  often  as  he 
cho'se,  and  the  statutes  generally  allow  a  collection  of  legal  in- 
terest as  often  as  WJIB  'agreed  upon  by  the  parties  in  the  original 
coniract.     They  alsc*'allow$;  collection  of  simple  interest  upon 
any  interest  money  a^t^it  becomes  due,  if  not  paid.      They 
also  allow  compounding  »t  the  legal  rate  as  often  as  the  debtor 
chooses,  provided  tha.t  thev-bld  obligation  be  cancelled  and  a 
new  one  given.     Compound  interest  then  is  not  of  itself  illegal., 
it  is  only  certain  forms  of  it. 

The  difficulty  attending  partial  payments  is  in  deciding 
whether  jfchey  shall  be  applied  to  the  debt  of  interest  or  princi- 
pal. If  applied  to  the  debt  of  principal,  there  is  only  simple 
interest ;  if  applied  to  the  debt  of  interest,  the  practical  effect 
is  that  of  compound  interest. 

The  Vermont  Rule  is  the  only  one  involving  no  compound 
interest.  The  objection  to  that  rule,  when  the  time  is  more 
than  one  year,  may  be  seen  in  the  fact  that  the  payments  may 
be  no  greater  than  the  interest  due  at  the  time  of  the  payment, 
and  still  if  the  payments  are  sufficiently  frequent,  and  the  note 
run  sufficiently  long,  the  entire  debt  of  principal  and  interest 


144  INTEREST. 

may  be  discharged,  and  the  holder  of  the  note  become  indebted 
to  the  debtor.  (See  Ex.  1,  page  143.)  Both  the  Mercantile  and 
the  United  States  Rules  involve  compound  interest,  the  former 
compounding  it  once  a  year,  the  latter  as  often  as  a  payment  is 
made  which  equals  or  exceeds  the  interest  then  due.  When  the 
"payments  occur  at  intervals  of  just  one  year,  commencing  with 
the  date  of  the  note,  bo  th  rules  give  the  same  result.  When  they 
occur  oftener  than  once  a  year,  the  Mercantile  Rule  is  the 
favorable  to  the  debtor  ;  when  more  than  a  year  intervenes, : 
United  States  Rule  is  tjpie  more  favorable.  The  Vermont  R 
is  usually  more  favorable  than  either,  for  by  that  there 
no  compound  interest,  and  all  the  payments  draw  interest. 
By  the  use  of  the  United  States  Rule  an  inducement  is  offtred 
to  defer  payment  as  long  as  possible,  and  the  longer  paying 
be  deferred,  the  greater  the  inducement  to  continue  it.  Strict 
justice  to  all  parties,  in  all  cases,  would  be  to  have  the  interest 
on  the  whole  debt,  whether  of  principal  or  interest,  compoum 
instantaneously.  This  method,  though  desirable,  can  not 

•<  O 

present  be  made  practicable.     See  Note,  page  118, 

Examples. 

1.  A  holds  an  obligation  against  B  for  $1000,  wnich 
run  25  years  at  Q%  interest.      At  the  expiration  of  each  year  a 
payment  of  $60  was  made.     What  is  the  amount  due,  as  com- 
puted by  each  of  the  rules  given  above  ? 

By  the  United  States  Rule,  B  owes  A  $1000. 
By  the  Mercantile  Rule,  B  owes  A  $1000. 
By  the  Vermont  Rule,  A  owes  B  $80. 

2.  A  note  of  $10000  runs  4  years  at  8$  interest,  on  which 
were  made  quarterly  payments  of  $500.     What  was  the  amount 
due  at  the  time  of  settlement  ? 

By  the  Vermont  Rule,  $4000. 

By  the  Mercantile  Rule,  $4322.30. 

By  the  United  States  Rule,  $4408.21. 
Note. — It  will  be  observed  that  generally  the  result  obtained 
by  the  Mercantile  Rule  will  be  intermediate  between  those  ob- 
tained by  the  other  two. 


INTEREST. 


145 


DIAGRAM 

ILLUSTRATING 

SIMPLE,   ANNUAL, 

AND 

COMPOUND  INTEREST. 


10 


146  INTEREST. 

SIMPLE    INTEREST. 

ART.  107.  The  relation  between  the  principal,  time,  rate  per 
cent.,  and  interest,  is  exhibited  to  the  eye  in  the  diagram  on  the 
opposite  page.  Let  the  single  line  A  (which  for  convenience  is 
separated  from  the  diagram,  but  which  should  be  considered 
as  extending  horizontally  to  the  left  from  B,  C,  D,  etc.,  re- 
spectively,) represent  the  principal ;  the  perpendicular  line  BG 
represent  time  with  its  divisions  into  years,  at  the  points  C,  D, 
E,  and  F;  and  the  horizontal  lines  CH,  DI,  EK,  FL,  and  GM 
the  accrued  simple  interest  at  the  expiration  of  each  successive 
year.  As  no  ratio  can  be  expressed  between  time  and  money, 
area  can  represent  nothing  in  the  diagram.  As  rate  per  cent. 
is  nothing  but  the  ratio  between  the  principal  and  interest,  it 
can  only  be  represented  by  the  degree  of  divergence  of  the 
lines  BC  and  BH,  by  which  the  lines  CH,  DI,  EK,  and  FL 
shall  bear  a  proper  relation  to  the  line  A.  If  the  rate  be  10$ 
per  annum,  the  line  CHrnust  be  TW  or  TV  of  the  line  A,  DI  r\, 
EK  T\,  and  so  on.  The  line  BM  represents  nothing  but  a  limit 
to  the  lines  representing  interest  for  any  time  on  the  line  BG. 

A  +  CH,  A+DI,  A+EK,  etc.,  represent  the  amount  due 
each  successive  year  at  simple  interest. 


ART.  108.      ANNUAL    INTEREST. 

Simple  and  annual  interest  are  the  same  for  the  first  year. 
At  this  time  in  "  annual  interest,"  the  accrued  simple  interest 
on  the  principal  forms  a  new  principal  to  draw  simple  interest 
till  maturity.  The  same  is  true  at  the  end  of  each  following 
year.  This  increase  of  interest  will  be  represented  by  the  lines 
/i,  JT3,  LG,  and  Mi  0.  The  rate  being  10^,  Ii  must  be  TV  of 
CH  its  principal;  JK"3  =  Tair  of  CH+T\  of  NI=T^  of  CH ; 
£«  =  •&  of  CH+fv  NI+j\  of  OK=T°v  of  CH;  and  M,  0  = 
TV  of  CH  +  T\  of  NI+  A  of  OK+  TV  of  PL  =  [£  of  CH=  CH. 
It  will  be  observed  that  the  line  B\  0  is  not  a  straight  line,  but 
composed  of  straight  lines,  the  degree  of  divergence  from  the 
line  BG  being  increased  at  the  end  of  each  year  ;  also  that  the 
numbers  i,  3,  c?  i »,  etc.,  are  the  sums  of  the  several  series  i  ; 


INTEREST.  147 

x 

i  +  2 ;  i  +  a  +  3  ;  1  +  2  +  3  +  4,  etc.  ;  and  also  that  they  express 
the  number  of  years  that  the  simple  yearly  interest  of  the  prin^ 
cipal  must  draw  interest  to  equal  the  interest  on  all  the  several 
amounts  of  annual  interest.  The  line  ab,  though  limited  by 
the  straight  line  6,  i  o,  is  still  a  correct  representation  of  the 
interest  due  at  the  end  of  4|  years  with  annual  interest. 


ART.  109.      COMPOUND     INTEREST. 

Annual  and  compound  interest  are  the  same  for  two  years. 
Then  the  interest  which  has  accrued  on  the  first  annual  interest 
becomes  a  part  of  the  principal.  In  like  manner  all  the  interest 
at  the  end  of  each  year  becomes  a  part  of  the  principal  for  the 
next  year.  The  line  ,,  c,  d,  2,  limits  the  horizontal  lines  re- 
presenting compound  interest  after  the  first  two  years.  It 
should  be  separated  from  the  line  Si  0  at  the  point  3,  a  distance 
equal  to  TV  of  /,.  At  the  point  6,  a  distance  equal  to  3c+  TV 
of  Kc.  At  the  point  i  „,  equal  to  6d+TV  of  Ld. 

Or,  comparing  simple  interest  with  compound,  the  line  B2 
must  begin  to  diverge  from  the  line  BM  at  the  point  H,  and 
be  separated  from  BM  at  the  point  7,  a  distance  equal  to  TV 
of  CN.  At  the  point  K,  equal  to  the  I,  +  TV  of  D  i .  At  the 
point  Lj  equal  to  Kc-}-  rV  of  EC.  At  the  point  M,  equal  to 


"PARTIAL    PAYMENTS"    ILLUSTRATED. 

ART.  110.  The  Diagrams  on  the  following  pages  illustrate 
the  difference  in  the  principle  of  the  three  foregoing  rules  for 
"  Partial  Payments." 

The  problem  used  in  each  diagram  is  the  following  : 

A  note  for  $1000  runs  4  years  with  interest  at  6$. 
In  1  yr.  frpm  date  a  payment  of      ...       $50  is  made. 
In  lj  yrs.  from  date  a  payment  of  .         .         .       250      " 
In  2  yrs.  from  date  a  payment  of     .         .         .       224      " 
In  2  yrs.  8  mo.  from  date  a  payment  of  .         .         20     " 
In  2  yrs.  10  mo.  from  date  a  payment  of.         .       110      " 

What  was  due  at  maturity  ? 


148  INTEREST. 

In  the  illustration,  time  is  measured  horizontally  by  the 
distance  between  the  perpendicular  lines. 

The  horizontal  base  line  in  each  figure  separates  principal 
from  interest,  the  perpendicular  lines  above  representing  the 
former,  and  those  below  the  latter.  The  perpendicular  lines 
above  are  limited  by  a  horizontal  line  which  is  more  or  less  re- 
moved from  the  base  line,  as  the  payments  are  applied  to  in- 
crease or  decrease  the  principal.  The  perpendicular  lines  below, 
representing  interest,  are  limited  by  a  line  always  diverging 
from  the  base  line,  the  degree  of  divergence  depending  upon 
the  rate  per  cent,  and  the  size  of  the  principal.  When  the 
entire  interest  is  cancelled  by  any  payment,  the  diverging  line 
starts  anew  from  the  horizontal  base  line.  The  perpendicular 
distance  between  these  two  limiting  lines  at  any  time  repre- 
sents the  amount  of  principal  and  interest  due  at  that  time. 


INTEREST. 


149 


$346. 


$476. 


10 


b    o 


^        S      r^      ^ 

•3l.^§ 


S950. 


Principal.  $10  00. 


O      -^     *'~~5  r5^     S^ 

l|?l,i: 

§  I.I.S 


s  ^ 


150 

i 


INTEREST 


$  489.19. 


$589.70. 


Jo 

ICO 


0      0 


fi  t§  i 

W  rd 

r^  -4— >  cQ 

5  - g 

<j  O  -1-3 


rj-j  M  QJ 

•§  ^  s 

5  G  S 

P^  R  g 

pi  o"  o 

•^  £  ^ 

^  3 

fH  +-  o 


o    ^ 


EH      ~ 
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152  CURRENCY     AND     MONEY. 

to  compounding  so  much  of  the  interest  then  due.  Had  the 
payments  been  more  frequent,  the  amount  due  at  maturity,  by 
the  United  States  Rule,  would  have  been  larger,  as  compared 
with  the  other  rules,  than  in  the  present  instance. 

It  is  recommended  to  the  pupil  to  study  these  diagrams  tiD 
he  becomes  perfectly  familiar  with  the  reason  why  different 
rules  give  different  results,  and  also  to  work  other  examples, 
drafting  diagrams  to  correspond.  With  the  use  of  proper 
mathematical  instruments,  tolerably  accurate  results  may  be 
obtained  by  drafting  alone.  Especially  should  the  pupil  notice 
that  rate  per  cent,  is  the  ratio  between  the  principal  and  in- 
terest, and  is  represented  in  the  diagram  by  the  degree  of 
divergence  of  the  interest  line  from  the  horizontal  base  line. 
In  the  same  diagram  the  less  the  principal,  the  less  the  diver- 
gence. 


CURBElNrCY    AND    MONEY. 

METALLIC  'CURRENCY. 

ART.  111.  BARTER  is  simply  exchanging  one  or  more  com- 
modities for  others,  as  giving  one  bushel  of  wheat  for  two 
bushels  of  corn. 

MONEY  is  an  instrument  to  facilitate  exchanges,  and,  strictly 
speaking,  should  possess  an  intrinsic  value  equivalent  to  that 
for  which  it  is  exchanged. 

Various  articles  have  at  different  times  and  by  different 
nations  been  used  for  this  purpose,  as  shells,  leather,  corn, 
cattle,  etc.,  but  the  precious  metals,  gold  and  silver,  have  been 
found  to  be  most  serviceable  for  the  following  reasons  : 

1st.  They  possess  great  value  in  small  bulk. 

2d.  Their  value  remains  quite  uniform,  changing  only  by 
slow  degrees. 

3d.  They  can  be  used  or  hoarded  without  much  wear  or 
decay. 


CURRENCY     AND     MONEY.  153 

4th.  The  pieces  can  be  united  or  subdivided  without  loss 
of  value. 

5th.  They  are  homogeneous  in  their  structure,  and  easily 
identified. 

Gold  and  silver,  by  being  used  as  money,  become  the  stand- 
ard of  reference  for  expressing  the  value  of  other  commodities. 
The  price  of  a  commodity  is  usually  its  value  expressed  in  the 
denominations  of  money. 

When  prices  or  obligations  in  debit  and  credit  and  barter 
are  thus  expressed,  and  business  transacted  without  the  inter- 
vention of  money,  we  have  what  is  called  the  "  money  of  ac- 
count." The  denominations  in  the  "  money  of  account"  may 
be  even  different  from  the  denominations  of  the  money  in  cir- 
culation, and  if  the  denominations  of  both  be  the  same,  the 
values  represented  by  them  may  be  different.  Still  further, 
there  may  be  a  "  money  of  account"  where  there  is  no  money 
in  actual  use,  in  which  case  (as  to  a  certain  extent  in  all  cases) 
prices  are  only  expressions  showing  the  relative  value  of  com- 
modities, and,  like  the  terms  used  in  the  measure  of  arcs  and 
angles,  are  indefinite  until  referred  to  other  commodities,  or  to 
the  same  commodity  of  different  amount.  Gold  and  silver 
have  an  intrinsic  value,  depending  upon  their  cost  of  produc- 
tion and  uses.  They  derive  a  value  from  their  capacity  to 
facilitate  exchanges,  just  as  horses,  mules,  and  railroads  derive 
their  value  from  facilitating  transportation.  Government  can 
no  more  create  a  value  to  gold  and  silver  than  to  sugar.  It 
does,  however,  increase  their  value  by  coining  them  into  pieces 
convenient  for  use,  and  declaring  them  legal  tender  in  payment 
of  debt.  Coinage  being  only  a  certificate  of  value  already  ex- 
isting in  the  metal,  it  is  not  necessarily  the  work  of  govern- 
ment, neither  is  legal  tender  a  necessary  element  of  even  a 
metallic  currency,  as  is  seen  in  the  coinage  of  copper  and  nickle. 
Coining  gold  and  silver  enhances  their  value  in  the  same  way 
that  manufacturing  steel  enhances  the  value  of  the  iron  used, 
or  as  the  brand  of  an  official  inspector  renders  certain  articles 
of  merchandise  more  salable.  Making  gold  and  silver  coins 
legal  tender  increases  their  value  because  it  increases  their 


154  CURRENCY     AND     MONEY. 

demand.  For  when  other  articles  of  value  can  not  be  used 
in  liquidating  indebtedness,  these  will  always  answer  the 
purpose. 

Money,  by  being  legal  tender,  becomes  naturally  a  standard 
of  value  for  other  property.  But  money  itself  is  not  an  invari- 
able measure  of  value,  for  the  reason  that  its  value,  like  that 
of  other  kinds  of  property,  is  affected  by  cost  of  production, 
supply,  demand,  etc.  The  debasement  of  coins  by  government 
is  not  here  taken  into  the  account.  If  gold  alone  were  used  as 
money  and  legal  tender,  its  gradual  change  of  value  would  be 
perceptible  only  as  it  caused  an  increase  or  decrease  of  prices. 
A  diminution  in  value  of  gold  would  raise  prices,  and  vice 
versa.  But  frequently  gold  and  silver  both  are  legal  tender,  as 
it  was  in  the  United  States  until  A.D.  1853.  In  making  both 
legal  tender,  it  is  necessary  for  government  to  establish  their 
relative  value.  If  the  legal  relative  value  be  the  actual  com- 
mercial relative  value,  then  both  will  circulate  equally  well, 
except  so  far  as  convenience  may  dictate.  But  as  both  are 
constantly  changing  in  their  commercial  value,  while  the  legal 
relative  value  remains  the  same,  the  metal  that  has  the  greatest 
commercial  value  will  be  used  to  make  foreign  purchases,  while 
the  cheaper  metal  will  remain  at  home.  It  is  a  general  prin- 
ciple in  currency,  that  if  several  different  articles  be  allowed  to 
circulate  as  money,  the  cheaper  will  displace  the  dearer.  If  a 
thousand  silver  dollars  will  pay  a  larger  debt  in  a  foreign  coun- 
try than  a  hundred  gold  eagles,  then  silver  will  be  shipped  in 
payment. 

By  making  silver  legal  tender  for  small  sums  only,  its  legal 
relative  value,  or  mint  valuation,  may  be  considerably  higher 
than  its  commercial  or  marketable  value,  and  still  the  currency 
will  not  be  burdened  by  its  abundance,  and  gold  will  be  re- 
tained for  the  reason  that  it  will  be  demanded  for  the  payment 
of  those  debts  that  are  above  the  silver  limit.  Whenever  both 
are  legal  tender  for  any  amount,  there  must  be  frequent  neces- 
sity for  government  to  change  the  legal  or  nominal  value.  In 
A.D.  1853,  silver  coins  in  the  United  States  were  made  "  legal 
tmderfor  all  sums  not  exceeding  Jive  dollars"  and  its  nominal 


CURRENCY     AND     MONEY.  155 

value  was  made  so  great  that  it  is  not  probable  there  will  be 
need  of  another  change  for  very  many  years,  if  ever.  The  same 
is  true  in  England. 


PAPER     CURRENCY. 

ART.  112.  Bank  notes,  certificates  of  deposit,  checks,  bills 
of  exchange,  etc.,  are  in  business  used  as  money,  but  are  not 
money.  They  are  representatives  of  money  when  an  equiva- 
lent amount  of  gold  and  silver  is  lying  idle,  and  the  paper  takes 
its  place  in  the  circulation.  Otherwise,  they  are  representa- 
tives of  indebtedness  merely,  and  the  man  who  receives  them  in 
payment  of  any  debt  has  only  given  up  one  claim  for  another 
which  may  perhaps  be  more  available.  Bank  notes,  actually 
representing  gold  or  silver  in  store,  may  be  used  with  profit, 
for  the  reason  that  the  coin  lying  in  the  vault  is  saved  from 
wear,  and  the  inconvenience  and  risk  attending  the  transfer  of 
large  sums  are  to  a  great  extent  avoided.  This  is  the  case  with 
the  certificates  of  deposit  that  are  used  by  the  associated  banks 
in  New  York  in  settling  their  balances  at  the  "  clearing  house/7 
It  has  been  strongly  advocated  by  some  that  a  "  gold-note 
currency"  on  such  a  basis  might  with  many  advantages  be 
issued  from  the  Sub-Treasury  of  the  United  States.  Bullion 
banks  might  also  be  formed  that  would  furnish  the  same  kind 
of  currency. 

When  gold  or  silver  is  received,  it  is  an  ultimate  payment, 
for  they  are  supposed  to  contain  intrinsically  an  equivalent 
value.  The  policy  of  a  paper  currency,  beyond  an  actual  specie 
basis,  is  a  question  upon  which  intelligent  political  economists 
disagree.  The  use  of  certificates  of  deposit,  checks,  bills  of 
exchange,  etc.,  greatly  facilitates  the  transaction  of  business 
and  reduces  the  amount  of  metallic  currency  needed.  To  make 
them  serviceable  and  reliable,  however,  they  should  not  be 
issued  as  a  basis  of  credit,  or  for  procuring  loans,  but  should 
arise  from  legitimate  business  transactions  in  which  the  drawee 


156  CURRENCY     AND     MONEY. 

has  previously  become  actually  indebted  for  the  amount  of  the 
bill. 

Examples  relating  to  Coins  and.  M!oney  of.A_cco\int. 

1.  If  a  pound  of  sugar  be  worth  a  half  a  peck  of  wheat, 
what  would  be  the  price  in  wheat  of  50  Ibs.  of  sugar  ? 

Ans.  6 1  bushels. 

2.  If  a  pound  of  sugar  be  worth  8  pounds  of  wheat  or  10 
yards  of  tape,  how  much  tape  can  be  bought  for  a  pint  of 
wheat,  a  bushel  of  wheat  weighing  60  Ibs.  ?      Ans.  !£{•  yds. 

3.  If  an  ounce  of  silver  be  worth  6400  ounces  of  iron,  how 
many  tons  of  iron  can  be  bought  with  3£  pounds  of  silver  ? 

,  Ans.  8 1  tons. 

4.  If  the  value  of  a  bushel  of  wheat  be  represented  by  1. 
what  would  be  the  value  of  5  bush.  1  pk.  3  qts.  ? 

Ans.  5H- 

5.  Before  the  federal  currency  was  established  by  Congress 
in  1786,  and  indeed  for  some  time  after,  the  denominations  in 
the  money  of  account  in  the  United   States  colonies  were 
pounds,  shillings,  and  pence,  as  in  England,  while  most  of  the 
coin  in  circulation  consisted  of  Spanish  silver  dollars,   their 
halves,  quarters,  and  sixteenths.     Owing  to 'the  scarcity  of 
metallic  currency,  and  the  fact  that  the  relative  value  of  the 
money  of  account,  compared  with  the  silver  dollar,  had  not  been 
generally  determined  or  agreed  upon,  remarkable  fluctuations 
in  the  money  of  account  arose,  varying  in  different  States,  so 
that  when  it  became  necessary  to  fix  their  relative  values,  it 
was  found  that  in  the  New  England  States  £1  or  20  shillings 
=3^  Spanish  dollars,  while  in  New  York  and  Ohio  £lr=:only 
2^    Spanish   dollars.      How  much   below  the   New  England 
standard  was  the  money  of  account  in  Ohio  ?          Ans.  25$. 

6.  Assuming  the  pound  sterling  of  Old  England  to  have 
been  equal  at  that  time  to  4f  Spanish  dollars,  as  is  stated  by 
some,  how  much  below  that  standard  had  the  New  England 
money  of  account  depreciated  ?  Ans.  25$. 

7.  Assuming  the  Spanish  dollar  to  equal  a    ollar  in  federal 
currency,  how  much  less  in  cents  would  an  article  cost  in  New 


CURRENCY     AND     MONEY.  157 

York  whose  price  was  7  shillings.,  than  in  New  England  where 
the  price  was  6s.  6d.  ?  Ans.  20  f  cts. 

8.  Paper  currency  frequently  occasions  great  fluctuations  in 
the  money  of  account.     Continental  money,  when  first  issued, 
was  very  nearly  par  with  silver.     In  1778  its  depreciation  was 
as  6  to  1,  in  1780  as  30  to  1,  in  1781  as  1000  to  1.    The  money 
of  account  would,  however,  soon  cease  to  follow  such  extreme 
fluctuations,  but  would  adopt  some  other  standard.     Assuming 
the  paper  currency  of  Chicago  to  have  depreciated  the  money 
of  account  2%  below  that  of  New  York  city,  how  much  more  in 
New  York  funds  would  an  article  be  worth  in  New  York  than  in 
Chicago,  the  price  in  each  place  being  $1000  ?    Ans.  §19.608. 

9.  In  1837  the  fineness  of  the  silver  dollar  United  States 
coin  was  changed  from  f  llvl  to  TO-O-?  but  its  weight,  which  was 
416  grains,  was  so  changed  that  the  amount  of  pure  silver  in 
the  coin  remained  the  same  as  before.     What  was  the  weight 
after  the  change  ?  Ans.  412^  grs. 

10.  In  1853  the  weight  of  the  silver  half-dollar  was  changed 
from  20fi{  grains  to  192  grains,  the  fineness  remaining  the 
same,  viz.,  /„.     What  is  the  value  in  new  silver  coin  of  the 
dollar  coined  before  1853  ?  Ans.  107f  J  cts. 

11.  From  1792  to   1834  the  United  States  eagle  weighed 
270  grs.,  and  was  }|  fine.     Its  weight  was  then  reduced  to 
258  grs.,  its  fineness  remaining  the  same.     In  1837  the  fineness 
was  reduced  to  T\,  the  weight  remaining  the  same,  since  which 
there  has  been  no  change.     What  is  the  present  value  of  an 
eagle  coined  previous  to  1834  ?  Ans.  $10.65 f^f. 

12.  Augustus  Humbert,  United  States  Assayer  in  Califor- 
nia, under  a  legal  provision  of  1850,  has  issued  fifty  dollar 
pieces  of  gold,  purporting  on  their  face  to  be  887  thousandths 
fine  and  weighing  1310  grains  each.     Assuming  them  to  be  of 
full  fineness  and  weight,  what  is  their  value  in  United  States 
gold  coinage  ?  Ans.  $50.05JH- 

In  the  above  examples  no  account  is  made  of  the  alloy. 

13.  If  I  take  20  Ibs.  of  bullion  of  standard  fineness  to  the 
mint  to  be  coined,  and  pay  a  seigniorage  of  \%,  what  amount 
of  money,  in  gold  coin,  should  I  receive  ?       Ans.  $4442.79. 


]  58  CURRENCY     AND     MONEY. 

14.  In  A.D.   671  a  pound   sterling  was  equivalent  to  a 
pound  Troy  of  silver.     In  the  14th  century  the  same  amount 
of  silver  was  coined  into  £1  5s.,  and  a  pound  of  gold  into  £15. 
After  successive  debasements  for  the  profit  of  kings,  a  pound 
of  silver  now  makes  £3  11s.  2d.,  and  a  pound  of  gold  makes 
£50  9s.  5d.     The  average  price  of  wheat  in  the  14th  century 
was  £1  for  what  now  averages  £2i.     Prices  of  other  staple 
commodities  and  wages  have  undergone  a  similar  change.    The 
conclusion  is  apparent,  that  though  governments  may  depre- 
ciate the  money  of  account,  they  can  not  force  the  sale  of  com- 
mon merchandise  at  much  less  than  its  value.     Though  they 
may  change  the  conditions  of  legal  tender,  so  that  6  shillings 
worth  of  silver  will  pay  a  pound  of  debt,  new  contracts  will 
recognize  the  change,  and  ultimately  not  be  affected  by  it. 
Queen  Elizabeth,  using  a  pound  of  silver  for  coining  £3  5s.  for 
England,  put  no  more  than  that  into  £8  for  Ireland.     What 
ought  to  have  been  the  price  of  flour  in  Ireland  for  what  in 
England  cost  £1  ?  Ans.  £2  9T33  shillings. 

15.  James  the  Second  manufactured  four  pennyworth  of 
silver  into  £10,  with  which  he  paid  off  his  soldiers.     What  per 
cent,  of  their  just  dues  did  they  receive  ?      Ans.  |  per  cent. 

16.  Suppose  an  estate  to  have  been  left,  centuries  ago,  for 
the  support  of  the  dean  of  a  cathedral  and  four  choristers,  the 
income  then  being  £300  per  year,  out  of  which  he  was  to  pay 
each  chorister  £30.     If  the  debasement  of  current  coin  has 
raised  rents  250/£,  and  the  increased  supply  of  the  precious 
metals  raised  it  150/£  more,  how  do  the  relative  salaries  of  the 
dean  and  choristers  compare  with  what  they  were  evidently 
designed  to  be  by  the  testator  ? 

Ans.  The  dean  should  receive  6  times  what  a  chorister  re- 
ceives, but  actually  receives  46  times  as  much. 


BANKS     AND     BANKING.  159 


BANKS  AND  BANKING-. 

ART.  113.  BANKS  are  of  four  kinds.  Banks  of  Deposit, 
Banks  of  Discount,  Banks  of  Issue,  and  Banks  of  Exchange. 
The  first  two  and  the  last  may  be  established  by  individuals  or 
associations,  the  other  only  by  special  authority  from  the  State. 


BANKS     OF     DEPOSIT. 

ART.  114,  BANKS  OF  DEPOSIT  are  for  the  safe  keeping  of 
money. 

A  special  deposit  is  made  when  the  identical  money  is  to 
be  returned  to  the  depositor,  the  bank  being  responsible  only 
for  the  safe  keeping ;  the  loss,  for  instance,  attending  the  failure 
of  the  banks  whose  notes  are  deposited  being  sustained  by  the 
depositor.  In  other  cases,  the  Lank  or  banker  becomes  in- 
debted to  the  depositor,  the  banker  being  allowed  to  use  the 
money  as  he  pleases,  but  obligating  himself  to  pay  the  depositor 
the  whole  or  any  part  of  the  amount  due  him  whenever  it  is 
demanded,  if  demanded  during  business  hours.  The  improba- 
bility that  all  the  depositors  of  a  bank  will  call  for  the  entire 
balance  of  their  account  at  the  same  time,  renders  it  safe  for 
the  banker  to  use  a  portion  of  the  funds  thus  entrusted  to  him, 
in  loaning  to  those  who  need  the  money  but  for  a  short  time, 
and  may  therefore  be  relied  upon  for  prompt  payment.  The 
interest  money  thus  received  is  the  banker's  compensation  for 
keeping  the  accounts  of  his  depositors.  Sometimes  interest  is 
paid  by  the  banker  for  the  deposit,  but,  as  a  general  rule,  that 
this  interest  may  be  refunded,  there  is  a  strong  temptation  to 
loan  too  large  an  amount  "  on  call,"  or  to  seek  largely  paying 
investments,  with  doubtful  securities,  which  is  against  the  in- 
terest of  both  banker  and  depositor. 

When  the  depositor  usually  has  a  large  balance  with  his 
banker,  there  is  an  implied  obligation  with  the  banker  to  give 


160  BANKS     AND     BANKING. 

such  a  customer  or  dealer  the  preference  in  "  bank  accommo- 
dation/' if  he  offer's  equally  good  security. 

The  advantages  to  a  business  man  in  keeping  a  bank  ac- 
count are  the  following : 

1st.  If  he  has  an  honest  prudent  banker,  his  surplus  funds 
are  ordinarily  safer  than  if  kept  by  himself. 

2d.  The  settlement  of  bills  with  checks  drawn  upon  bankers 
is  not  only  more  convenient,  but  there  is  less  liability  of  error, 
and  if  errors  do  occur,  the  vouchers,  which  should  always  be 
preserved,  will  aid  in  detecting  them. 

3d.  He  will  lose  less  from  counterfeit,  broken,  and  uncur- 
rent  money,  and  will  be  relieved  from  frequent  charges  of  pay- 
ing out  the  same  by  throwing  the  responsibility  upon  his 
banker. 

4th.  By  depositing  his  Bills  Receivable  and  Drafts,  he 
avoids  much  trouble  and  risk  attending  their  collection.  If  by 
mistake,  oversight,  or  neglect,  drawers  and  endorsers  are  re- 
leased from  liability,  tho  banker,  by  assuming  the  collection, 
becomes  responsible  for  the  consequences. 

5th.  It  aids  him  in  establishing  his  own  credit,  and  learning 
the  credit  and  responsibility  of  others  with  whom  he  wishes  to 
do  business. 

The  Bank  of  Hamburg  is  exclusively  a  bank  of  deposit,  the 
silver  in  the  vault  always  being  equal  to  the  amount  of  the 
deposits.  This  may  be  withdrawn  at  pleasure  by  the  deposit- 
ors, but  the  business  is  mostly  done  by  checks,  which  have  the 
effect  merely  of  transferring  the  credits  from  one  account  to 
another.  The  expenses  of  the  bank  are  met  by  a  small  per- 
centage charged  the  depositors  on  the  amount  of  business  done. 
The  currency  of  Hamburg  being  almost  exclusively  silver,  ex- 
changes are  greatly  facilitated  through  the  means  of  this  insti- 
tution. 


BANKS     AND     BANKING.  161 

BANKS    OF    DISCOUNT. 

ART.  115.  Banks  of  Discount  are  closely  connected  with 
Banks  of  'Deposit ,  and,  indeed,  they  generally  exist  together  in 
the  same  institution.  Their  ohject  is  the  loaning  of  money,  the 
discount  being  the  interest  taken  in  advance.  The  capital  may 
1)  .-long  to  one  individual,  or  to  a  company  forming  a  copartner- 
ship, or  to  a  corporation  organized  by  authority  of  the  State. 
The  securities  usually  taken  are  endorsed  names,  stocks,  bonds, 
and  business  paper.  The  primary  object  of  banks  of  discount  be- 
ing to  grant  temporary  loans,  where  the  business  requires  at  some 
seasons  more  capital  than  can  be  profitably  employed  through 
the  year,  and  to  aid  in  preserving  an  equilibrium  in  such  regu- 
lar business  as  may  be  disturbed  by  irregularity  of  receipts  and 
disbursements,  it  is  unwise  to  depend  upon  such  institutions 
for  any  portion  of  the  permanent  capital  needed  in  business. 
Continued  loans  and  renewals  from  a  bank  of  deposit  are  very 
unreliable.  For  when  the  bank  calls  for  payment  to  supply 
the  withdrawal  of  deposits  it  will  generally  be  found  to  be  just 
the  hardest  time  to  pay. 


BANKS    OF    ISSUE. 

ART.  116.  Banks  of  Issue  are  those  institutions  that,  by 
authority  of  the  general  government,  put  in  circulation,  to  be 
used  as  money,  their  own  notes,  payable  on  demand  in  gold  or 
silver  coin.  When  payable  at  some  future  specified  time,  they 
are  called  post  notes.  Were  banks  of  issue  to  retain  in  their 
vaults  sufficient  gold  or  silver  to  redeem  all  their  circulating 
notes  at  once,  there  would  be  no  profit  to  them  from  the  circu- 
lation except  so  far  as  the  notes  should  be  lost  or  destroyed, 
and  never  presented  for  redemption,  which  has  been  found  to 
amount,  extraordinary  losses  excepted,  to  about  one  tenth  of 
one  per  cent,  per  annum.  If,  on  the  other  hand,  they  were 
loaned  as  money,  and  no  actual  capital  kept  idle  to  redeem 

them,  the  banker  would  receive  the  same  revenue,  until  their 

11 


162  BANKS     AND     BANKING. 

redemption,  as  lie  would  from  an  equivalent  amount  of  capital 
furnished  him  in  gold  and  silver.  In  short,  his  credit  would  at 
all  times  afford  him  as  much  working  capital  as  his  notes  in 
circulation  amount  to. 

The  value  of  bank  notes  as  currency  depends  upon  the  ease 
and  certainty  with  which  they  may  be  converted  into  gold  or 
silver  coin.  Hence  the  importance  of  rigid  restrictions  being 
imposed  by  government  to  insure  a  prompt  and  certain  re- 
demption. Without  these  the  field  is  open  to  frauds,  limited 
only  by  the  intelligence  and  forbearance  of  the  community. 

The  paper  currency  of  our  country  is  furnished  by  twenty- 
seven  different  States,  each  under  somewhat  different  laws  and 
regulations.  In  general,  they  can  be  classified  under  three  dif- ' 
ferent  systems,  a  specie  basis,  a  safety  fund,  and  the  "free 
banking"  principle. 

The  specie  basis  requires  a  part,  or  all  its  capital,  to  be  paid 
in  coin,  limits  the  amount  of  circulation  in  proportion  to  its 
capital  paid  in,  and  makes  the  assets  of  the  bank,  with  per- 
haps the  individual  liability  of  the  stockholders,  furnish  the 
means  to  redeem  the  circulating  notes. 

The  "safety  fund"  system  requires  each  of  several  banks  to 
deposit,  with  a  State  officer  or  Board  of  Control,  a  certain  per- 
centage of  its  capital  or  circulation,  which  shall  be  safely  in- 
vested as  a  "  bank  fund"  to  redeem  the  notes  of  any  insolvent 
bank  that  may  have  contributed  its  due  proportion  for  this 
purpose. 

In  "free  banking"  the  circulating  notes  are  secured  by  State 
stocks,  to  at  least  an  equivalent  amount  at  their  marketable 
value.  The  stocks  are  deposited  with  an  officer  of  State,  for 
which  he  issues  registered  blank  notes.  These,  when  signed, 
are  used  as  money  by  the  banker,  while  he  receives  at  the  same 
time,  the  interest  on  the  stocks  deposited.  If  the  bank  fails 
to  redeem,  the  stocks  are  sold,  and  the  proceeds  applied  to  the 
redemption. 


E  X  C  H  A  N  G<E  .  163 

BANKS    OF    EXCHANGE. 

ART.  117.  Nearly  all  banks  are  Banks  of  Exchange,  their 
legitimate  business  being  the  buying  and  selling  of  drafts,  by 
which  remittances  and  settlements  of  debt  at  distant  places 
are  made  without  the  transmission  of  money.  The  operation 
of  this  department  of  banking  will  be  more  full  explained  un- 
der the  subject  of  "  EXCHANGE."  Those  bankers  who  deal 
exclusively  in  buying  and  selling  gold,  silver,  and  bank-notes, 
are  called  "  brokers"  or  "  money  brokers." 


EXCHANG-E. 

ART.  118.  When  a  purchase  is  made  a  satisfactory  equiva- 
lent is  rendered  by  the  purchaser  in  various  ways.  It  may  be 
by  labor  or  services,  or  he  may  give  other  commodities  in  ex- 
change, which  last  transaction  is  called  barter.  He  may  give 
gold  and  silver,  which  are  also  commodities  of  an  equivalent 
value,  but  called  money,  because  they  are  serviceable  mainly 
in  making  other  purchases,  thereby  facilitating  several  trans- 
actions in  barter.  Frequently,  however,  no  equivalent  is  ren- 
dered ;  but  an  obligation  merely  on  the  part  of  the  purchaser 
for  a  fixed  amount  is  recognized  by  both  purchaser  and  seller. 
This  constitutes  debt  on  the  part  of  the  purchaser,  and  credit 
on  the  part  of  the  seller,  and  is  expressed  in  the  denominations 
of  the  "  money  of  account."  If  now  the  debtor  gives  a  writ- 
ten obligation  to  pay,  in  the  form  of  a  due  bill  or  promissory 
note,  this  evidence  of  credit  with  the  holder  may  he  transferred 
as  other  property,  and  another  become  the  creditor.  In  book- 
keepifig,  the  account  with  the  seller  is  closed,  and  "  Bills  Pay- 
able" receives  the  credit.  Instead  of  giving  his  own  promissory 
note,  he  may  use  those  which  he  himself  has  received  in  the 
same  way  ;  as  for  example,  bank  notes  which  were  issued  ex- 
pressly for  this  kind  of  circulation.  When  bank-notes,  or 
certificates  of  deposit,  are  held  as  evidence  of  debt  against  a 
bank,  the  debt  is  collected  by  the  return  of  these  to  the  bank 


164  EXCHANGE. 

If  it  be  an  account  current,  and  kept  by  a  pass-book,  it  is  sub- 
ject to  drafts  or  checks. 

The  facility  with  which  business  is  transacted  by  means  of 
drafts  or  other  paper  substitutes,  for  money,  has  given  to  the 
term  Exchange  a  technical  use,  and  now  signifies  the  method 
of  making  payments  at  distant  places  ~by  the  use  of  Drafts  or 
Bills  of 'Exchange ,  without  the  transmission  of  money.  The 
business  is  usually  transacted  through  bankers,  who  buy  the 
credits  payable  in  distant  places,  and  sell  to  those  having  pay- 
ments to  make  in  those  places. 

To  illustrate,  suppose  the  pork  dealers  of  Cincinnati  to  send 
their  pork  to  New  York  for  sale,  and  receive  therefor  gold, 
which  is  returned  to  them  by  express.  Suppose  also  the  dry- 
goods'  merchants  of  New  York  to  send  their  goods  to  Cin- 
cinnati for  sale,  and  receive  therefor  gold,  which  is  returned  to 
them  by  express.  If  the  pork  purchasers  in  New  York  had 
paid  the  dry-goods'  merchants  there,  and  the  dry-goods'  pur- 
chasers in  Cincinnati  had  paid  the  pork  dealers  there,  the  whole 
business  might  have  been  closed  without  the  risk  and  expense 
of  transmitting  gold  either  way.  This  would  be  done  by  the 
pork  sellers  drawing  drafts  or  orders  on  the  pork  buyers,  in 
favor  of  the  dry-goods'  buyers,  who,  having  paid  for  these  drafts, 
would  forward  them  to  the  dry-goods'  sellers  in  payment  of 
their  purchase.  These  drafts  being  presented  to  the  pork  buy- 
ers would  be  cashed,  and  thereby  the  debts  arising  in  both 
cities  liquidated  without  the  transmission  of  any  money.  In 
making  this  system  general,  to  include  all  kinds  of  trade  in 
many  different  places,  it  would  frequently  be  very  difficult 
for  those  having  bills  of  exchange  to  sell  to  find  buyers,  and 
vice  versa.  An  exchange  broker,  or  bank  of  exchange,  will 
obviate  this  difficulty.  They  bring  the  buyers  and  tscllers 
together,  by  buying  bills  with  their  own  capital,  and  sending 
them  forward  for  credit,  then  selling  their  own  drafts  drawn 
against  this  credit,  in  amounts  to  suit  purchasers.  If  between 
any  two  places  the  amount  of  bills  bought  equal  those  sold, 
then  no  gold  need  be  transmitted,  and  the  difference  between 
the  buying  and  selling  rate  would  be  the  commission  charged 


PAR     OF      EXCHANGE.  1C.1) 

by  the  broker  for  his  services,  use  of  his  capital,  and  risk  in 
buying  such  drafts  as  would  not  be  honored. 


PAH    OF    EXCHANGE. 

ART.  119.  To  understand  the  quotations  of  premium  or 
discount  in  exchange,  it  is  necessary  to  consider  the  currencies 
of  the  different  places.  Supposing  gold,  as  a  metal,  to  be  so 
distributed  as  to  have  in  all  places  a  uniform  intrinsic  value, 
and  gold  coin  to  be  the  only  currency,  the  true  par  of  ex- 
change between  two  countries  is  the  exact  equivalent  of  gold  in 
the  standard  coin  of  one  country  compared  icith  the  gold  in 
the  coin  of  the  other.  If,  however,  gold  is  the  standard  of  cur- 
rency in  one  country,  and  silver  in  the  other,  the  relative  in- 
trinsic values  must  be  compared.  This  need  be  computed  only 
when  the  coins  and  money  of  account  in  the  two  countries  are 
different.  Comparing  the  sovereign  of  England  with  the  half 
eagle  of  America,  for  instance,  we  find  the  sovereign  to  weigh 
123.3  grains,  but  only  916^  thousandths  of  it  pure  gold.  The 
half  eagle  weighs  129  grains  and  900  thousandths  pure  gold. 
If  we  reduce  the  fineness  of  the  sovereign  to  that  of  the  half 
eagle,  without  changing  its  value,  it  must  weigh  125  rWV 
grains.  In  this  estimate  the  alloy  is  reckoned  of  no  value. 
To  ascertain  the  true  equivalent  we  have  this  simple  propor- 
tion, 129  grains  :  125.583  grains  :  :  §5  :  §4.SG7j. 

As  the  weight  and  fineness  of  the  sovereigns  coined  previously 
to  the  present  reign  were  somewhat  less  than  the  value,  as  de- 
rived above,  the  average  value,  as  fixed  by  our  mint,  is  $4.84 
A  new  Victoria  sovereign,  however,  is  worth  §4.86  f.  A  pound 
sterling  (£)  is  a  denomination  in  the  money  of  account  only ; 
the  sovereign  is  a  coin  of  an  equivalent  value.  It  follows  from 
the  above  that  exchange  on  London  is  par  when  a  bill  for 
£100  can  be  bought  for  §486.75  in  American  gold. 

The  common  quotations  are  based  upon  a  purely  nominal 
value  of  the  pound  sterling,  viz.  :  $4.44£,  for  that  is  not  now 
its  value  in  any  other  sense. 


166  STERLING     EXCHANGE. 

True  value  of  the  pound  sterling,     .         .         .     $4.8675 
Nominal       "  "  ...       4.4444  + 

Difference=9i^  (nearly)  of  the  nominal  par,  .  .4230 
When  the  quotations  are  109^,  sterling  exchange  is  really 
at  par  ;  when  110/£,  it  is  at  a  premium  ;  when  109^,  it  is  at  a 
discount.  Quotations  are  generally  made  on  sterling  bills 
drawn  at  60  days'  sight.  As  the  cost  of  transmitting  gold,  in- 
cluding insurance,  is  about  equal  to  the  interest  on  the  bill  for 
60  days,  the  time  for  the  passage  of  both  being  the  same,  re- 
mittances often  are  made  in  these  time  drafts,  for  which  the 
same  is  paid  as  for  sovereigns  of  equivalent  amount. 


RULE     FOB    COMPUTING-    STERLING- 
EXCHANGE. 

ART.  120.  To  $40  add  the  premium  on  $40,  at  the  quoted 
rate.  By  this  sum  multiply  the  amount  of  sterling  exchange 
expressed  in  pounds,  and  divide  the  product  by  9.  The  quo- 
tient will  be  the  value  in  dollars. 

E  x  a  m.  pie. 

What  will  a  bill  for  £224  5s.  6d.  cost  in  New  York  when 
sterling  exchange  is  par,  quoted  at  109^  or  §\%  premium  ? 

£224  5s.  6d.  40 

43.8  9i#=  3.80 

~179T~  43.80 

672 
896 

10.95 
1.095 

9)9823.245 
$1091.47    Aw. 

By  comparing  French  coin  with  that  of  the  United  States, 
we  find  20  francs  Louis  Napoleon  equal  to  $3.84,  or  one  dollar 
in  gold  equal  to  5  francs  and  21  centimes  nearly,  or  5r\V 
francs.  The  quotations  of  Paris  exchange  are  usually  made 
in  this  way,  without  involving  percentage.  If  a  bill  of  ex- 


NOMINAL    ^EXCHANGE.  167 

change  for  more  than  521  francs  can  be  bought  for  $100,  Paris 
exchange  is  at  a  discount ;  if  less,  it  is  at  a  premium,  and  the 
quotations  express  the. number  of  francs  that  can  be  thus 
bought. 

The  sum  mentioned  in  a  bill  of  exchange  on  a  foreign 
country  is  usually  expressed  in  the  denominations  of  the  money 
of  account  in  the  place  where  it  is  made  payable.  Computa- 
tions in  foreign  exchange  therefore  require  the  use  of  tables  of 
foreign  money,  including  the  comparative  values  of  the  coins 
or  currencies  in  those  countries. 


NOMINAL    EXCHANGE. 

ART.  121.  In  the  United  States,  though  the  money  of  ac- 
count be  nominally  the  same,  yet  owing  to  the  character  of 
the  paper  money  in  circulation,  the  currencies,. and  hence  the 
moneys  of  account  of  different  states  and  cities,  are  essentially 
different.  The  relative  value  of  paper  money,  as  stated  here- 
tofore, depends  upon  the  risk  and  cost  of  converting  it  into 
coin. 

If,  for  example,  in  Buffalo,  it  costs  \%  to  convert  the  usual 
paper  currency  into  coin,  the  true,  par  of  exchange  between 
that  city  and  New  York  (where  coin  only,  or  its  equivalent,  is 
current)  would  be  expressed  by  the  nominal  rate  of  \%  pre- 
mium, in  favor  of  New  York.  For  the  same  reason  the  cur- 
rency of  Chicago  being  redeemable  in  coin  at  still  greater  cost, 
exchange  on  New  York  may  actually  be  at  par  when  the  nomi- 
nal rate  is  2^  premium.  This  2^  no  more  expresses  the  actual 
premium  than  does  the  9^  the  actual  premium  of  exchange 
on  London.  It  is  really  the  premium  of  New  York  currency 
over  Chicago  currency.  The  true  value  of  the  denominations 
in  our  money  of  account  is  represented  by  coin  only,  being 
established  by  the  law  regulating  legal  tender.  Practically, 
however,  by  the  use  of  a  depreciated  local  currency,  the  money 
of  account  for  that  place  is  equally  depreciated.  Thus,  goods 
bought  in  New  York  for  §100,  when  sold  in  Chicago  for  $100 


168  NOMINAL     EXCHANGE. 

are  sold  for  less  than  their  cost,  counting  transportation  and 
insurance  nothing.  Prices,  however,  will  tend  to  appreciate 
as  tha  value  of  the  currency  depreciates,  so  that  the  apparent 
loss  by  an  unfavorable  nominal  exchange  is,  in  general,  compen- 
sated by  increased  prices.  Inasmuch  as  increasing  the  supply 
of  even  a  metallic  currency  depreciates  its  relative  value,  the 
nominal  exchange  between  two  places,  using  the  same  kind  of 
currency,  with  the  same  mint  standard,  will  be  in  favor  of  the 
place  having  the  smallest  amount  of  currency  in  proportion  to 
its  business  wants,  and  therefore  having  the  least  depreciation. 
The  nominal  exchange  is  then  measured  by  the  excess  of  the 
market  price  of  bullion  above  the  mint  price,  and  is,  so  far, 
unfavorable.  A  depreciation  of  metallic  currency  which  affects 
the  nominal  exchange  may  also  be  occasioned  by  abrasion  or 
wear  of  circulation,  or  by  making  only  one  of  two  metals  legal 
tender  where  the  other  is  in  general  circulation.  It  will  be 
observed  that,  although  this  "  exchange,"  which  is  merely  nom- 
inal, almost  universally  enters  into  the  quotations  of  exchange 
between  different  countries,  it  belongs  rather  to  the  exchange 
of  currencies  in  the  same  country,  and  expresses  the  difference 
between  the  current  and  the  standard  moneys  of  that  place. 

Agio,  meaning  "  difference/'  is  the  proper  term  to  express 
this  nominal  exchange  when  considered  alone.  In  the  United 
States  the  expense  of  sending  coin  to  and  from  New  York,  by 
the  modern  express  companies,  being  so  trifling,  the  premium 
on  New  York  exchange  must  always  bo  very  nearly  the  same 
as  on  coin.  The  fluctuations  in  the  nominal  rate  of  exchange, 
or  agio,  where  a  depreciated  paper  currency  is  used,  will  be 
much  greater  than  if  the  currency  were  coin  or  its  equivalent, 
for  the  reason  that  the  depreciation  will  be  more  variable. 
Sometimes  the  scarcity  of  such  currency,  compared  with  busi- 
ness wants,  raises  its  current  value  temporarily  to  nearly  par 
with  coin.  Just  so  far  the  nominal  exchange  disappears.  In 
Bank  notes  that  can  be  converted  into  coin  at  less  expense 
than  the  usual  local  currency  are,  for  that  place,  at  a  pre- 
mium. Those  costing  more  are  at  a  discount,  and  are  called 
uncurrent.  Indeed,  these  notes,  when  removed  from  their 


COURSE     OF     EXCHANGE.  169 

native  habitation,  resemble  bills  of  exchange  on  the  places 
where  they  are  redeemed,  and  are  bought  and  sold  at  nearly 


the  same  rates  as  exchange. 


COURSE    OF    EXCHANGE. 

ART.  122.  Having  ascertained  the  par  of  exchange  we  have 
a  basis  for  computation.  The  nominal  exchange  modifies  that 
computation,  by  showing  the  relative  value  of  the  metallic 
currency  affected  by  scarcity  and  abundance  or  abrasion,  and 
also  the  depreciation  arising  from  the  use  of  a  paper  currency 
not  equivalent  to  coin,  though  bearing  the  same  denomination 
in  the  money  of  account. 

The  course  of  exchange  relates  to  the  relative  supply  and 
demand  for  bills,  or  the  relative  amount  of  indebtedness  be- 
tween different  countries  or  cities.  If  the  debts  and  credits 
between  two  countries  are  equal,  the  real  exchange  is  at  par, 
if  unequal  it  will  fluctuate  with  the  inequality.  If  New  York 
owes  London  more  than  London  owes  New  York,  bills  on  Lon- 
don will  bo  at  a  premium.  The  range  of  this  course  of  ex- 
change will  be  limited  by  the  expense  of  transmitting  coin  or 
bullion,  and  the  premium,  cannot  for  a  long  time  exceed  that 
expense.  The  current,  or  computed  rate  of  exchange,  includes 
both  the  real  and  nominal  exchange,  taking  the  true  par  for  a 
basis.  "Within  the  United  States  it  is  reckoned  by  percentage. 
Between  the  United  States  and  England  it  is  reckoned  also  by 
percentage,  but  the  true  par  is  at  a  premium  above  an  assumed 
fictitious  par.  So  that  an  advance  in  quotation  from  109  to 
110  is  not  really  1$,  that  is,  one  on  a  hundred,  but  less,  it 
being  only  1  on  109^. 

With  other  countries  the  current  exchange  is  generally  ex- 
pressed by  equivalents,  thus  $1=5  francs  15  centimes,  1  marc 
banco =35^  cts.  If  the  depreciation  of  Chicago  currency  be 
V/c,  and  the  real  exchange  on  New  York  \%  premium,  the 
current  rate  will  be  the  sum  of  the  nominal  and  real,  viz.  : 


170  BALANCE     OF      TRADE. 

\\%  premium.  If?  however,  the  real  exchange  be  \%  in  favor 
of  Chicago,  the  current  rate  will  be  equal  to  the  difference,  or 
\%  premium. 

The  equilibrium  in  the  course  of  exchange  is  only  to  a  small 
extent  restored  by  the  shipment  of  coin  or  bullion,  for  the  rea- 
son that  almost  always  other  articles  of  merchandise  can  be 
shipped  with  more  profit,  gold  and  silver  bearing  a  nearly  uni- 
form value  among  all  civilized  nations.  When,  however,  new 
productive  mines  are  opened  and  worked,  the  metals  depreciate 
in  value  in  the  mining  country,  in  which  case  they  become 
profitable  articles  of  export  to  non-producing  countries,  until 
the  depreciation  becomes  general.  The  unequal  depreciation 
occasions  a  variation  in  the  nominal  exchange  before  the  coin 
or  bullion  is  shipped.  The  transfer  of  the  metal  would  affect 
the  real  exchange,  because  it  either  pays  or  creates  a  debt. 


"BALANCE    OF    TBADE." 

ART.  123.  If  a  country,  in  her  trade  with  other  nations, 
buys  more  than  she  sells,  so  as  to  incur  a  debt,  the  payments 
of  which,  in  bullion  Or  coin,  would  reduce  the  amount  of 
metallic  currency  below  her  proper  proportion,  as  compared 
with  the  supply  in  other  nations,  she  is  said  to  "  over- trade," 
and  the  "  balance  of  trade"  is  against  her.  If  the  reverse  be 
true,  the  balance  of  trade  is  in  her  favor.  Some  restrict  the 
term  "  balance  of  trade"  to  the  exchange  of  commodities  other 
than  gold  or  silver.  But  why  should  not  gold  be  considered  a 
staple  article  of  export  from  California  and  Australia,  as  iron 
is  from  Sweden  or  lumber  from  Maine  ?  It  is  not  proposed 
here  to  discuss  this  subject  in  its  bearing  upon  the  prosperity 
of  a  country,  but  merely  to  offer  a  few  suggestions  to  Iho 
student,  in  its  relation  to  the  subject  of  exchange.  It  is  raihei 
the  balance  of  payments  between  separate  countries,  and  the 
mode  of  estimating  the  amount,  the  direction,  and  means  of 
liquidating  it,  that  ho  should  consider  here.  1st.  Although 


BALANCE     OF     TRADE.  171 

the  direct  commerce  between  two  separate  nations  may  be  very 
unequal,  yet  the  total  amount  of  importations  to  any  country 
are  for  the  most  part  paid  for  by  its  exportations,  through  the 
agency  of  bills  of  exchange,  drawn  against  the  latter,  and 
transmitted  to  other  countries  in  payment  of  the  former. 
Sometimes  it  is  effected  by  a  succession  of  bills  drawn  by 
bankers  through  intermediate  points,  or  a  more  circuitous 
route,  which  gives  rise  to  Circular  Exchange  and  an  Arbitra- 
tion of  Exchange.  For  example,  a  merchant  in  New  York 
may  remit  to  Hamburg  by  buying  first  a  bill  on  Paris,  and 
then  by  his  agent  another  on  London,  and  there  a  bill  on  Ham- 
burg. Kemittances  to  remote  points  are  more  frequently  made 
by  bankers'  bills  drawn  on  some  commercial  center,  where 
other  bankers  are  accustomed  to  keep  an  account,  so  that  they 
may  be  easily  negotiated,  making  the  place  thereby  a  kind  of 
clearing-house.  Thus,  London  has  been  styled  "  the  clearing- 
house of  the  world."  Nearly  all  our  foreign  trade  is  settled 
through  England  and  France.  In  like  manner,  remittances 
between  inland  towns  in  the  United  States  are  made  in  drafts 
on  New  York.  The  course  of  exchange  between  London  and 
New  York  does  not  arise  alone  from  the  commerce  between 
the  two  cities,  but  from  all  that  commerce  that  is  settled  for 
through  those  places.  Thus,  if  we  pay  for  our  importations 
of  tea  with  bills  on  London,  our  balance  of  payments  with 
London  is  affected  the  same  as  if  the  tea  came  directly  from 
London. 

2d.  So  far  as  the  commerce  of  any  country  is  carried  on  by 
its  own  capital  and  labor,  a  large  share  of  the  excess  of  imports 
over  the  exports  arises  from  the  profit  of  the  trade,  which  does 
not  increase  the  balance  of  payments.  If,  for  example,  an 
American  vessel  leaves  New  York  for  Liverpool,  with  a  cargo 
of  wheat,  valued  at  §10,000,  which  is  sold  there  for  §12;000, 
and  that  amount  invested  in  manufactured  goods,  and  taken 
to  China  and  sold  for  §15,000,  and  that  amount,  with  §5,000 
cash  invested  in  tea,  which  is  brought  home  to  New  York,  it 
is  evident  that,  from  that  transaction,  the  importations  exceed 
the  exportations  $10,000,  one  half  of  which  represents  the 


172  BALANCE     OF     TRADE. 

gross  profit  for  the  round  trip,  not  including  the  enhanced  value 
of  the  tea  by  being  transported  from  China  to  New  York. 

3d.  So  far  as  foreign  vessels,  sustained  by  foreign  capital 
and  labor,  transport  our  exports  and  imports,  the  difference 
between  the  two,  as  valued  at  our  own  ports,  will  show  the 
balance  of  payments. 

4th.  Goods  lost  at  sea  have  been  entered  at  the  Custom 
House  whence  they  cleared  as  exports.  But  if  the  loss  is  sus- 
tained by  the  exporting  country,  they  pay  for  nothing  abroad, 
and  foreign  exchange  is  affected  no  more  than  if  destroyed 
before  shipment.  If  the  loss  be  sustained  by  the  country 
whither  they  were  bound,  exchange  is  affected  the  same  as  if 
they  had  reached  their  destination. 

5th.  When  capitalists  emigrate  from  one  country  to  another, 
so  far  as  they  carry  their  capital,  either  in  coin  or  goods,  with 
them,  the  real  exchange  is  not  materially  affected  ;  but  if  they 
remove  their  capital  through  the  agency  of  certificates  of  de- 
posit, letters  of  credit,  or  their  own  bills  of  exchange,  it  becomes 
a  debt  of  one  country  to  the  other,  which,  in  the  end,  is  gener- 
ally paid  in  merchandise  rather  then  money.  This  fact  often 
affects  sensibly  the  course  of  exchange  between  the  east  and 
west  of  the  United  States. 

6th.  The  negotiation  of  bonds,  stocks,  and  other  loans  in 
a  foreign  country  creates  a  debt  against  that  country,  which, 
though  nominally  for  money,  is  generally  paid  in  merchandise. 
After  this  debt  is  paid,  though  the  bonds  are  truly  the  evi- 
dence of  debt  against  the  country  that  issued  them,  yet,  with 
the  exception  of  the  payment  of  the  interest,  the  balance  of 
payments  and  course  of  exchange  are  not  affected  ti]l  the  ma- 
turity of  the  bonds. 

7th.  An  excess  of  imports  over  exports,  as  shown  by  the 
Custom  House  returns,  by  no  means  prove  that  a  country  is 
in  debt.  Indeed,  it  is  clear  from  what  has  been  stated,  that 
with  every  nation  engaged  in  the  carrying  trade  the  imports 
will  generally  exceed  the  exports,  and,  so  far  as  the  latter  pay 
for  the  former,  the  greater  the  excess  the  more  profitable  the 
commerce. 


STATISTICS.  173 

The  fluctuations  in  the  rate  of  exchange  depend  upon  a 
variety  of  conditions,  a  few  only  of  which  have  here  been 
noticed.  They  cannot,  to  any  great  extent,  be  controlled  by 
an  arbitrary  decree  of  bankers  or  merchants.  Excepting  when 
disturbed  by  a  panic,  or  an  unusual  distrust  in  the  credit  of 
those  who  draw  or  accept  bills  of  exchange,  which  gives  it  a 
fictitious  value,  the  current  rate  represents  the  actual  resultant 
of  all  the  movements  in  trade  and  currency,  whether  traceable 
or  not,  and  is,  therefore,  if  properly  analyzed,  a  better  test  of 
the  condition  of  accounts  between  different  countries  and  cities 
than  any  estimate  that  can  be  made,  independent  of  it,  based 
upon  exports  and  imports  and  other  Custom  House  data. 

To  understand  the  current  rate,  however,  requires,  as  stated 
before,  a  thorough  knowledge  both  of  the  par  of  exchange  and 
the  nominal  rate,  for  frequently  the  fluctuations  in  the  cur- 
rent rate  are  wholly  due  to  the  fluctuations  in  the  nominal 
rate,  which  latter  depends  entirely  upon  the  relative  condition 
of  the  currency. 


STATISTICS. 

ART.  124.  To  exhibit  the  truth  of  the  foregoing  principles, 
a  few  statistics  have  been  compiled  from  reliable  authorities. 

Total  imports  to  the  United  States,  includ- 
ing bullion  and  specie,  from  1790  to 
1857,  inclusive,  ....  $7,658,722,496 

Total  exports  for  the  same  time,     .         .       6,860,004,549 
Excess  of  imports  for  68  yrs.  ending  1857,     "798/717,947 
7  "  36,363,971 

30  "        1850,       250,438,055 

31  "       1820,       511,915,921 
The  valuation  of  imports,  as  obtained  from  Custom  House 

returns,  owing  to  the  ad  valorem  system  of  tariff,  is,  below 
their  cost,  generally  estimated  to  average  even  10^.  It  will  be 
observed  that  allowing  an  undervalution  of  \%  will  increase 
the  excess  of  imports  about 


174 


STATISTICS. 


Excess  of  imports  of  bullion  and  specie  for 

30  years  ending  .1850,  before  the  supply  of 

gold  from  California,  .         .         .   *     .          $69.995.789 

Excess  of  exports  of  bullion  and  specie  for  7 

years  ending  1857,     .         .         .         .         .          269.797.1G8 

From  1790  to  1820  the  imports,  including  bullion  and 
specie,  exceeded  the  exports  each  year  except  in  1811  and  1813. 
From  1821  to  1857  the  imports  exceeded  the  exports  each  year 
except  in  1821-5-7,  1830,  1840-2-3-4-7,  1851-5-6-7. 

Total  amount  of  public  and  corporation  debt  held 
in  foreign  countries  against  the  United  States 
in  the  form  of  bonds,  stocks,  &c.,  is.  generally 


estimated  at, 


$300,000,000 


On  which  there  is  probably  paid  an  annual  divi- 
dend of  about,       20,000,000 

The  average  current  rate  of  exchange  on  England  at  New 
York,  for  No.  I  bankers'  bills,  as  quoted  on  the  first  of  each 
month  was,  for — 


1822  .  . 

12   1831 

8f 

1840  .  . 

8 

1849  ..   9 

1823  .  . 

7^ 

1832 

9 

1841   .  . 

?* 

1850  ..   9 

1824  .. 

9~ 

1833 

8 

1842  .  . 

7? 

1851   ..   10 

1825  .. 

81 

1834 

..   31 

1843  .  . 

<i 

1852  ..   10 

1826  .  . 

10 

1835 

Of 

1844  .  . 

9 

1853  .  .   9 

1827  .  . 

103 

1836 

8 

1845  .  . 

91 

1854  .  .   9 

1828  .. 

101 

1837 

..  13* 

1846  .  . 

8J 

1855  .  .   9 

1829  .  . 

9 

1838 

*  *       4 

1847  .. 

h? 
4 

1856  ..   9 

1830  .  . 

n 

1839 

..   91 

1848  .  . 

9j 

1857  (to  Sept.)  9 

Average  for  the  9  years  ending  1830, 
"     10          "  1840, 

"     10          "  1850, 

"       7          "  1857, 


It  will  be  perceived  that  the  average  rate  of  sterling  ex- 
change at  New  York,  for  the  twenty  years  ending  1850,  was 
\%  below  par,  or  \%  in  favor  of  New  York ;  while,  for  the 
seven  years  following,  it  was  above  par,  or  in  favor  of  England. 

Of  the  $300,000,000  of  gold  deposited  at  the  Mint  and 
branches,  and  Assay  Office  at  New  York,  for  the  six  years  ending 
1855,  about  94^  per  cent,  was  produced  by  California. 

In  San  Francisco  sight  exchange  on  New  York  averages 


EXAMPLES     IN     EXCHANGE.  175 

about  3^  premium,  the  currencies  of  both  places  having  a 
metallic  basis. 

If  we  put  900  new  sovereigns  and  900  new  shillings  into 
average  ordinary  circulation,  in  12  months  time  the  former 
will  be  worth  about  899  and  the  latter  about  894. 

In  London,  previous  to  the  re-coinage  in  1774,  exchange 
was  uniformly  about  2$  in  favor  of  Paris,  owing  to  the  fact 
that  the  old  coinage,  by  wear,  had  sunk  below  its  standard 
weight  about  2$,  while  the  coinage  of  France  was  not  thus  de- 
graded. As  soon  as  the  new  coinage  took  the  place  of  the  old, 
exchange  became  par.  Before  the  re-coinage,  in  the  reign  of 
William  III,  owing  to  the  wear  and  clipping  of  the  silver 
coins,  the  nominal  exchange  between  England  and  Holland 
was  25/b  against  England,  while  at  the  same  time  the  real  ex- 
change was  in  her  favor,  as  was  shown  upon  the  issue  of  the 
new  coins. 


EXAMPLES   RELATING  TO   EXCHANGE. 

ART.  125.  1.  What  is  the  cost  of  a  draft  on  New  York 
for  $1250,  the  rate  of  exchange  being  \\%  premium  ? 

Ans.  $1268.75. 

2.  What  must  be  the  face  of  a  draft  to  cost  $1000,  at  f 
per  cent,  premium  ?  Ans.  $993.79. 

Remark. — For  a  strictly  accurate  solution  assume,  say  $1, 
for  the  face,  and  find  its  cost,  then  by  it  divide  the  given  cost. 
Custom,  however,  allows,  for  small  sums,  the  percentage  to  be 
computed  on  the  cost  instead  of  the  face.  By  that  rule  the 
answer  to  the  last  question  would  be  $993.75.  The  ap- 
proximation may  be  brought  nearer  by  adding  the  premium 
on  the  premium,  which,  in  this  case,  is  \%  of  $6.25= §0.04 
nearly. 

3.  What  would  be  the  proceeds  of  $4000  invested  in  ex- 
change on  New  Orleans,  at  a  premium  of  \%  ? 

\%  of  $4000=^20,  and  \%  of  $20= $0.10. 
$4000- $20  + $0.10= $3980. 10,  Ans. 


176          EXAMPLES  IN  EXCHANGE. 

If  the  rate  had  been  \%  discount  we  should  havo  had 
$4000  +  $20 + $0.10= $4020~.  10. 

4.  What  must  be  paid  in  New  York  for  a  draft  on  London 
for  £1374  5s.  9d.,  at  10%  premium  ?  Ans.  $6718.74. 

5.  What  amount  of  sterling  exchange  can  be  bought  for 
$3122.25  the  premium  being  9f^  ?     Ans.  £640  Is.  lUd 

Find  by  the  rule  the  cost  of  £1,  by  which  divide  the  given 
cost. 

6.  What  will  a  draft  on  Paris  for  12144.5  frcs.  cost  if 
$1=5.35  frcs.  ?  Ans.  $2270. 

7.  What  will  be  the  cost,  at  Milwaukie,  of  a  bill  on  Lon- 
don for  £1500,  the  quotation  at  New  York  being  110,  the  agio 
of  Milwaukie  current  funds  being  2%  discount  compared  with 
those  of  New  York,  and  the  real  exchange,  or  course  of  ex- 
change, being  \%  in  favor  of  New  York  ?       Ans.  $7498.33. 

8.  New  York  quotations  of  Paris  exchange  being  5.18  frcs., 
and  the  agio  of  Cincinnati  current  funds  being  1%  discount 
compared  with  United  States  coin,  what  will  a  bill  of  1000 
frcs.  cost  at  Cincinnati,  if  the  purchaser  buys  coin  and  sends 
by  express,  at  a  charge  of  $1.50  per  thousand  dollars,  and 
buys  the   exchange  in   New  York   through  a  broker  whose 
charges  are  \%  for  commission  ?  Ans.  $195.75. 

9.  The  money  of  account  in  Hamburg  is  of  two  kinds,  each 
reckoned  in  marcs  or  marks,  viz  :  marks  banco  and  marks 
current.     The  former  is  the  account  kept  at  the  bank  where 
specie  or  bullion  is  deposited,  and  is  generally  the  standard  of 
reference  in  quotations  of  exchange.     The  latter  is  current  in 
business,  and  is  much  depreciated,  the  agio  of  the  two  accounts 
being  subject  to  slight  variations.     The  par  of  exchange  be- 
tween Hamburg  and  London  is  1  mark  banco=ls.  5{d.     As- 
suming £l=:$4.S6f ,  what  is  the  par  of  exchange  between  Ham- 
burg and  New  York  ?     Ans.  1  mark  banco=35i  cts.  nearly. 

10.  Assuming  the  quotations  of  109^  on  London  and  35 J 
on  Hamburg  to  represent  the  par  of  exchange,  as  they  do  very 
nearly,  how  much  per  cent,  higher  is  Hamburg  exchange 
sterling  exchange,  when  the  quotations  are  110  and  36. 

Ans.  .9518$. 


EXAMPLES    IN    EXCHANGE.  177 

11.  Assuming  the  mark  current  at  Is.  2d.  sterling,  what  is 
the  agio  between  the  two  moneys  of  account  at  Hamburg  ? 

Ans.  The  mark  banco  would  be  25/^  premium. 
It  usually  varies  from  20  to  26^  premium. 

12.  What  would  be  the  cost,  at  Chicago,  of  a  bill  on  Ham- 
burg for  10,000  marks  banco,  the  banker  in  Chicago  drawing 
direct,  at  New  York  quotations  (37  cts.  per  mark),  adding  the 
current  rate  of  exchange  on  New  York  (\\%  premium),  and 
\%  commission  ?  Ans.  $3792.50. 

13.  If  the  agio  between  New  England  paper  currency  and 
coin  be  \%,  and  between  Illinois  currency  and  coin  2$,  what 
would  it  be  if  both  circulated  in  equal  proportions  ? 

Ans.  \{%. 

14.  If  the  currency  in  circulation  in  Cincinnati  have  an 
agio  of  \%  compared  with  United  States  coin,  what  would  be 
the  ultimate  effect  of  making  Illinois  currency  "  bankable"  if 
its  agio  is  2$. 

Ans.  It  would  drive  from  circulation  every  thing  but  Illi- 
nois currency  or  its  equivalent,  and  depreciate  the  money  of 
account  \\%. 

15.  A  banker  in  New  York  sends  1000  eagles  to  London, 
at  a  cost  for  freight  and  insurance  of  |^,  which  is  paid  in  New 
York,  and  receives  credit  at  the  rate  of  £3  16s.  2d.  per  oz., 
and  3/o  per  annum  interest  on  the  account.     At  the  same  time 
he  sells  a  60  days'  sight  bill  drawn  against  the  proceeds  of  the 
coin  and  the  accrued  interest,  at  the  rate  of  110^.     Suppose 
the  bill  to  be  accepted  on  the  day  of  the  credit,  and  payable 
without  grace,  what  profit  does  the  banker  receive  in  the  trans- 
action. Ans.  $28.20. 

16.  At  one  time  the  laws  of  Spain  rigidly  restrained  the  ex- 
portation of  the  precious  metals  from  that  country,  still  they 
were  secretly  exported  at  a  risk  of  about  2$.     What,  then, 
was  the  nominal  exchange  between  that  and  other  countries 
having  a  free-trade  in  bullion,  arising  from  the  depreciation 
occasioned  by  relative  excess  ?     Ans.  About  2$  against  Spain. 

17.  If  from  the  large  increase  of  California  gold,  or  exces- 
sive paper  issues  in  the  United  States,  the  nominal  exchange 


178          EXAMPLES  IN  EXCHANGE. 

between  England  and  the  United  States  should  be  2$  in  favor 
of  England,  what  should  be  the  quotations  of  sterling  ex- 
change, other  things  being  equal,  to  represent  the  balance  of 
payments  in  equilibrium  ?  Ans.  \\\\%. 

18.  If  the  nominal  exchange,  at  London,  on  Hamburg,  be 
16 \%  discount,  what  would  a  London  merchant  make  for  his 
net  profit,  the  cost  of  transportion,  insurance,  &c.,  being  5^  on 
the  purchase  price,  and  payable  at  London,  if  he  sells  in  Ham- 
burg for  £12,000  what  cost  in  London  £10,000  ? 

Ans.  He  would  lose  £500. 

19.  If  the  currencies  of  England  and  the  United  States 
were  in  due  proportion  in  amount  compared  with  business 
wants,  what  would  be  the  effect  upon  the  "  movement"  of 
the  precious  metal  between  the  two  countries,  if  the  United 
States  should  add  to  its  currency  a  large  issue  of  paper  money 
or  gold  coinage,  thereby  raising  prices  and  depreciating  the 
relative  value  of  money  ? 

20.  Why  is  any  country  better  able  to  sustain  an  increase 
of  importations  compared  with  the  exportations,  when  it  arises 
from  an  excess  of  specie  currency,  than  when  it  arises  from  an 
excess  of  paper  currency  ? 

Ans.  Because  nothing  but  metal  will  pay  the  balance,  and 
in  the  one  case  we  can  afford  to  part  with  it,  while  in  the  other 
we  cannot. 

21.  Suppose  the  circulating  medium  in  San  Francisco  to  be 
depreciated  below  the  currency  of  New  York  Y/o  in  consequence 
of  imperfect  coinage,  and  the  expense  of  transportation,  includ- 
ing risk,  be  \%  more,  and  the  broker's  commission  in  New 
York  be  \%,  what  does  an  exchange  broker  or  gold  exporter 
in  San  Francisco  make,  if  he  sells  sight  drafts  on  New  York 
for  3%  premium,  and  to  make  his  exchange  he  is  obliged  to 
ship  gold  ?  Ans.  \l%. 

22.  If  a  wheat  merchant  in  Toledo  buys  wheat  at  $1.00 
per  bushel,  and  sends  it  to  Buffalo  for  sale  at  $1.02^  per 
bushel,  the  cost  for  transportation,  insurance,  and  commission 
being  ~\.\%,  what  per  cent,  profit  does  he  make,  if,  in  view  of  the 
difference  in  value,  or  agio,  of  the  currencies  of  the  two  places, 


EXAMPLES  IN  EXCHANGE.          179 

he  is  able  to  negotiate  at  \%  premium  the  drafts  drawn  against 
the  proceeds  of  the  sale  ?  Ans.  1^. 

Remark. — In  the  last  example  the  rates  were  made  to  cor- 
respond with  those  of  the  21st,  to  show  more  clearly  to  the 
pupil  that  in  general  the  same  laws  govern  the  movement  cf 
gold  in  large  quantities  as  regulate  the  movements  of  wheat. 

23.  During  the  year  ending  June  30,  1857,  our  exports,  in- 
cluding specie,  to  England,  exceeded  our  imports  from  England 
§54,216,623 ;    but  in  our  trade   with    Cuba,   Brazil,   China, 
and   France,  our  imports  exceeded  our  exports,  as  follows  : 
Cuba,  §30,319,658  ;  Brazil,  $15,915,526  ;  China,  $3,961,802  ; 
France,  $9,553,840.     During  the  same  time  our  total  excess 
of  exports  of  specie  was  $56,675.123,  of  which  $46,821,211 
went  to  England,  and  we  will  suppose,  for  this  example  and 
the  one  following,  that  the  balance  of  excess  went,  in  equal 
amounts,  to  the  other  four  countries.     Why  did  the  specie  go 
to  England,  when  we  were  not  in  debt  to  her,  and  how  was 
our  debt  to  the  other  countries  probably  settled  ? 

24.  First,  Suppose  the  last  example  to  represent  our  entire 
foreign  commerce  and  trade  for  that  year,  after  a  full  settle- 
ment, and  to  include  nothing  else,  and  our  due  proportion  of 
specie  for  currency  to  have  been  preserved  by  supply  from 
California,  and  the  Custom  House  value  to  be  the  exact  ex- 
changeable values  of  both  importations  and  exportations,  what 
was  the  balance  of  net  profit  as  shown  by  the  excess  of  im- 
ports ?  Ans.  $5,534,203. 

Second,  What  per  cent,  would  that  profit  be  on  the  entire 
exports  to  those  countries  which,  for  that  year,  specie  included, 
were  about  $240  millions  ?  Ans.  About  2  j£. 

Third,  If  the  exports,  as  entered  at  the  Custom  House, 
not  including  specie,  were  $170,000,000,  and  the  imports,  as 
received,  were  entered  $231,000,000,  what  was  the  balance  of 
payments  in  specie,  if  the  exports,  being  carried  by  American 
vessels,  brought  in  the  foreign  market  10^  advance  on  their 
Custom  House  valuation,  and  the  imports  were  entered  5%  be- 
low their  cost  ?  Ans.  $56,157,895. 
Actual  balance  of  payments,  $56,675,123. 


180  BILLS     OF     EXCHANGE. 

Fourth,  If  our  due  proportion  of  currency  required  no  in- 
crease of  specie  for  the  year  1857,  and  California,  with  other 
American  mines,  furnished  for  the  market  §49,000,000,  how 
was  our  balance  of  trade  for  that  year  ? 

Ans.  $7,675,123,  against  us. 

Fifth,  Suppose  we  had  redeemed,  during  that  year,  of  our 
foreign  indebtedness  in  stocks  and  bonds,  §10,000,000,  what 
would  then  have  been  our  balance  of  trade  ? 

Ans.  §2,324,877  in  our  favor. 


BILLS    OF    EXCHANGE. 

ART.  126.  A  bill  of  exchange  is  an  order  or  draft,  made 
by  one  person  upon  a  second,  to  pay  a  certain  sum  of  money 
to  a  third,  or  to  his  order,  or  to  the  bearer.  For  example  : 


CLEVELAND,  0.,  Nov.  6,  1858. 

Sixty  days  after  date,  pay  to  the  order  of  J.  F.  Whitelaw 
one  thousand  dollars,  and  place  to  the  account  of 

To  Messrs.  SMITH  &  BROWN,  ALBERT  CLARK. 

New  York. 

The  person  making  the  order  is  called  the  drawer ;  the 
person  to  whom  the  order  is  addressed  is  called  the  drawee  ; 
and  the  one  to  whom  the  amount  is  payable  is  called  the  payee. 
If  the  drawee  accepts,  by  writing  his  name  across  the  face  of 
the  bill,  under  the  word  "  accepted,"  he  then  becomes  an 
acceptor,  and  the  instrument  is  then  called  an  acceptance.  Jf 
the  payee  writes  his  name  upon  the  back  of  the  instrument, 
he  becomes  an  indorser.  The  person  to  whom  it  is  afterward 
transferred  by  indorsement  is  called  an  indorsee. 

Foreign  bills  are'  those  which  are  drawn  in  one  country  but 
are  payable  in  another. 

Domestic  or  inland  bills  are  those  that  are  payable  in  the 
country  where  they  are  drawn. 

The  United  States  being  separate  sovereignties,  are  foreign 
to  each  other,  and  bills  drawn  in  one  payable  in  another,  like 


PROMISSORY     NOTES.  181 

the  example  given  above,  are  foreign  bills,  though  apparently 
inland. 

Time  bills  are  those  requiring  payment  at  a  certain  speci- 
fied time  after  sight  or  after  date.  All  others  are  payable  on 
demand.  When  time  bills  are  drawn  "acceptance  waived," 
they  may  be  held  till  maturity  before  being  presented  to  the 
drawee  ;  otherwise,  they  should  be  presented  immediately  for 
acceptance. 


PROMISSORY    NOTES.. 

ART.  127.  A  promissory  note  is  a  written  agreement  by 
one  party  to  pay  to  another  a  specified  sum  at  a  specified  time. 
The  one  making  the  agreement  or  signing  the  note  is  called  the 
maker.  The  person  to  whom  the  amount  is  payable  is  called 
the  payee,  and  the  owner  of  the  note  is  called  the  holder.  A 
principal  is  one  directly  responsible  for  the  payment  of  a  bill 
or  note  a£  maturity. 

For  different  forms  of  notes,  see  examples  under  the  sub- 
ject of  Interest. 

Adjoint  and  several  note  is  one  signed  by  two  or  more  dis- 
tinct parties,  in  which  case  each  one  becomes  liable  as  maker 
or  principal,  the  same  as  if  no  others  signed  with  him.  Some 
of  the  features  of  a  valid  promissory  note  are  the  following : 

A  full  consideration  is  implied  from  the  nature  of  the  in- 
strument, but  a  want  of  consideration  would  be  a  valid  defense 
on  the  part  of  the  maker  as  against  the  payee,  but  not  as 
against  any  other  holder,  into  whose  possession  it  may  have 
come  without  a  knowledge  of  such  want  of  consideration,  in 
which  case  he  would  be  called  an  innocent  holder. 

It  may  be  written  with  ink  or  pencil,  or  it  may  all  be 
printed  except  the  signature,  which  must  always  be  in  the 
hand-writing  of  the  maker  or  his  authorized  agent.  It  should 
be  an  unqualified  promise  to  pay  in  money,  definite  in  amount, 
and  independent  of  all  contingencies.  The  amount  should  be 
expressed  in  the  body  of  the  note,  in  words,  and 'should  be  re- 
lied on  for  accuracy  rather  than  figures  in  the  margin. 


182  NEGOTIABLE     PAPER. 

If  the  time  is  not  definitely  stated,  it  is  payable  on  demand. 
If  the  place  of  payment  is  not  specified  it  is  payable  at  the 
place  of  business  or  residence  of  the  maker. 

In  the  settlement  of  bills  of  exchange  and  promissory  notes, 
so  far  as  their  terms  are  subject  to  general  law,  as  fixing  the 
rate  of  legal  interest  and  day  of  maturity  for  example,  the  law 
of  the  State  where  they  are  made  payable  should  govern.  If 
a  note  is  not  paid  at  maturity,  it  continues  to  draw  the  same 
interest  as  before,  if  it  does  not  exceed  the  legalized  rate  ;  but 
if  no  rate  be  mentioned,  it  draws  simple  interest  at  the  legal 
rate  till  paid. 


NEGOTIABLE    PAPER. 

ART.  128.  Bank  notes,  checks,  certificates  of  deposit,  bills 
of  exchange,  and  promissory  notes,  when  properly  drawn,  are 
negotiable,  except  when  made  payable  by  the  terms  of  the 
contract,  to  one  person  only.  If  the  amount  is  payable  to 
"bearer,"  or  is  subject  to  the  "order"  of  the  payee,  they  are 
negotiable.  But  if  neither  the  word  "  bearer"  nor  "  order"  ap- 
pears in  the  instrument,  but  simply  the  name  of  the  payee,  it 
is  not  negotiable,  and  the  payee  cannot  give  full  title  to  a  third 
party ;  for  the  account,  as  between  the  maker  and  payee,  would 
still  be  subject  to  a  garnishee  process  from  other  creditors  of 
the  payee. 

In  the  negotiation  of  paper  the  transfer  may  be  made  by 
delivery  or  ~by  indorsement.  If  payable  to  "  bearer,"  or  to  the 
payee  "  or  bearer,"  as  are  bank  notes  and  most  checks,  the 
transfer  is  by  delivery.  If  payable  "  to  the  order  of"  the 
payee,  or  to  the  payee  "  or  order,"  the  transfer  is  by  indorse- 
ment. 

If  the  payee  simply  writes  his  name  across  the  back  of  the 
paper  it  is  an  indorsement  in  blank,  and  is  afterward  negoti- 
able by  delivery.  But  if  above  this  indorsement  it  be  made 
payable  to  the  order  of  another  person,  called  an  indorsee,  it  is 
an  indorsement  in  full,  and  is  then  negotiable  only  by  the  in- 


NEGOTIABLE     PAPER.  183 

dorsement  of  the  indorsee.  By  repeating  this  kind  of  indorse- 
ment there  may  be  several  indorsees.  When  the  indorsement 
is  in  blank,  any  legal  holder  is  allowed  to  write  that  above  it, 
which  will  make  it  an  indorsement  in  full.  A  qualified  in- 
dorsement is  one  that  affects  the  liability  of  the  indorser,  but 
not  the  negotiability  of  the  paper,  as  when  made  "without  re- 
course." 


LIABILITY   OF  PARTIES  CONNECTED 
WITH   NEGOTIABLE   PAPER. 

ART.  129,  Bank  notes  designed  to  circulate  as  money, 
checks,  and  other  paper  negotiable  by  delivery,  may  be  legally 
retained  by  an  innocent  holder,  who  receives  them  in  good  faith 
for  a  valuable  consideration,  though  the  party  from  whom  they 
were  received  obtained  them  fraudulently. 

Bank  notes  are  a  good  tender  if  not  objected  to  at  the  time 
of  payment,  unless  it  should  appear  afterward  that  they  were, 
at  the  time  of  payment,  worthless,  or  of  less  value  than  repre- 
sented, as  when  counterfeit,  altered,  spurious,  broken,  or  un- 
current.  Any  unreasonable  delay  to  return  them,  after  the 
discovery  is  made,  whereby  the  payer  loses  the  opportunity 
or  means  of  indemnity,  would  throw  the  loss  upon  the  payee 
or  holder,  on  account  of  the  neglect. 

If  a  person  receives  a  check  on  a  bank,  it  is  his  duty  to 
present  it  for  payment  at  the  bank  during  the  same  or  the 
next  day  at  the  furthest;  otherwise  he  holds  it  at  his  own  risk, 
tha  loss  being  his  if  the  bank  fails  meantime,  provided  that  the 
funds  were  there  to  meet  the  check  before  the  failure.  If  he 
lives  at  a  distance  from  the  bank  he  must  send  it  for  collection 
by  mail,  or  otherwise,  during  the  same  or  next  day.  If  the 
check  passes  through  the  hands  of  several  persons,  each  one  is 
allowed  one  day,  and  his  liability,  so  far  as  above  described, 
ceases  with  the  succeeding  day.  Bank  drafts,  or  "  bankers' 
exchange,"  from  their  service  in  making  remittances  to  distant 
points,  may  be  used  to  fulfill  that  mission,  but  should  not  be 


184  NEGOTIABLE     PAPER. 

allowed  to  lie  still  or  circulate  as  money  beyond  the  reasonable 
expectation  of  the  drawer. 

When  the  holder  of  a  check  gets  it  certified  as  good  by  a 
bank  on  which  it  is  drawn,  the  drawer  is  released  though  the 
bank  fail  to  pay. 

As  between  the  maker  and  payee  of  a  note  the  maker  is 
allowed  any  defense  that  would  be  allowed  in  any  other  debt 
between  the  two.  But  as  between  the  maker  and  indorsee,  or 
other  holder,  no  defense  can  be  set  up,  except  it  be  shown  that 
the  holder  had  knowledge,  at  the  time  of  the  note's  coming  into 
his  possession,  of  a  just  ground  of  defense  between  the  maker 
and  payee.  If,  however,  the  note  came  into  the  possession  of 
the  holder,  after  it  became  due,  the  claim  of  the  holder  would 
be  subject  to  all  the  equities  in  favor  of  the  maker  that  existed 
at  maturity,  or  that  had  arisen  after  maturity. 

On  a  promissory  note  the  maker  is  principal,  and  is  directly 
responsible  to  any  bona  fide  holder.  The  indorsers  are  re- 
sponsible in  the  order  of  their  indorsements,  that  is,  each  one 
to  all  those  who  follow,  on  condition  of  their  being  duly  noti- 
fied of  non-payment,  as  explained  hereafter.  The  liability  of 
those  who  indorse  as  guarantors  is  not  so  easily  discharged 
by  a  failure  to  give  prompt  notice  of  non-payment. 

A  bill  of  exchange  involves  no  direct  liability  until  pre- 
sented for  acceptance.  If  acceptance  be  refused  by  the  drawee, 
the  drawer  immediately  becomes  principal,  and  is  bound  to  re- 
deem the  draft  from  the  holder  without  delay,  though  it  be  a 
time  draft,  and  the  time  not  yet  expired.  If  the  bill  be  ac- 
cepted, the  acceptor  becomes  principal,  the  same  as  the  maker 
of  a  promissory  note,  in  which  case  the  drawer  sustains  practi- 
cally the  position  of  first  indorser,  in  case  of  non-payment  on 
the  part  of  the  acceptor.  The  liability  of  indorsers  on  bills  is 
the  same  as  of  those  on  promissory  notes.  That  liability,  how- 
ever, may  be  avoided  in  both  cases  by  their  writing  over  their 
indorsements  "  without  recourse,"  or  other  words  of  equivalent 
signification,  except  so  far  as  to  wan-ant  that  the  bill  or  note 
is  genuine,  that  is,  not  forged  or  fictitious,  a  liability  which 
attaches  not  only  to  all  indorsers,  but  to  all  who  negotiate 


PROTEST.  185 

the  paper  by  delivery,  as  owners,  or  even  as  agents,  unless  thac 
agency,  with  the  name  of  the  principal,  be  distinctly  stated  at 
the  time  of  the  transfer. 

Indorsers  are  also  released  from  liability,  if  they  are  not 
duly  notified  of  non-acceptance  or  non-payment,  the  paper 
having  been  duly  presented. 

If  a  man  lends  his  name  and  credit  by  making  a  note  or  ac- 
cepting a  bill  of  exchange  for  the  accommodation  of  another 
party,  it  is  called  an  accommodation  paper.  He  thereby  be- 
comes liable  to  any  bona  fide  holder,  to  the  same  extent  as  if 
he  had  received  a  full  consideration,  except  to  the  person  for 
whose  accommodation  the  credit  was  given.  But  for  his  in- 
demnity for  payment  he  has  a  valid  claim  on  the  party  ac- 
commodated. 


PRESENTMENT,  PROTEST,  AND  NOTICE. 

ART.  130.  The  limits  of  this  work  will  not  allow  the  de- 
tail of  all  the  particulars  necessary  to  be  observed  by  the  holder 
of  a  bill  or  note,  in  making  a  proper  demand  for  payment,  and, 
in  case  of  non-payment,  in  properly  notifying  the  indorsers,  so 
that  they  may  not  be  released  from  liability.  The  importance 
of  the  subject  demands  the  careful  study  of  those  who  deal  in 
negotiable  paper,  or  who  undertake  the  collection  of  it  for 
others.  Business  men,  unless  thoroughly  posted,  had  better 
intrust  their  collections  with  some  responsible  banker.  A  few 
brief  rules  only  will  be  given. 

There  should  be  no  unnecessary  delay  in  presenting  for 
payment  any  paper  payable  on  presentation,  and  for  accept- 
ance all  time  drafts  (unless  drawn  "acceptance  waived"), 
especially  if  the  time  of  maturity  is  to  be  determined  by  the 
time  of  sight  or  presentment. 

When  the  time  is  definitely  fixed  by  the  date  of  the  in- 
strument or  of  the  acceptance,  it  must  be  presented  for  pay- 
ment on  the  exact  day  of  maturity,  as  regulated  by  the  law  of 


186  DAYS     OF     GRACE. 

the  State  where  it  is  made  payable.  A  protest  on  any  other 
day  would  be  of  no  avail. 

The  paper  itself  must  be  presented  by  the  holder  personally 
to  the  acceptor  Xor  maker,  or  their  authorized  agent,  at  the 
place  where  it  is  made  payable,  during  reasonable  business 
hours.  If  no  such  person  or  agent  is  found  with  funds  to  meet 
it,  the  paper  may  be  treated  as  dishonored.  In  case  of  non- 
acceptance  or  non-payment  the  paper  should  be  protested,  and 
the  drawer  and  indorsers  notified. 

"  A  protest  is  a  solemn  declaration  on  behalf  of  the  holder, 
drawn  up  by  an  official  person,  against  any  loss  to  be  sustained 
by  the  non-acceptance  or  non-payment  of  a  bill."  This  pro- 
test should  be  made  by  a  notary  public,  who  should  also  per- 
sonally make  due  presentment  or  demand,  and  should  on  the 
same  day,  or,  at  furthest,  the  next  day,  send  written  notices 
of  protest  to  the  parties  to  be  notified.  If  the  residence  of  all 
the  indorsers  be  not  known,  and  all  the  notices  be  sent  under 
one  cover  to  the  last  indorser,  he  is  allowed  only  one  day  to 
forward  the  notices  to  antecedent  indorsers.  So  also  for  each 
of  the  others.  Sundays  and  legally  recognized  holidays  are 
excepted.  Notices  to  parties  residing  in  the  same  town  must 
be  delivered  in  person  or  by  a  messenger.  Notices  to  all  others 
must  be  sent  by  mail.  If  an  indorser  writes  over  his  name 
"  waiving  demand  and  notice/'  a  protest  is  not  necessary  to 
retain  his  liability. 


DAYS  OF  GRACE  AND  TIME  OF  MATURITY. 

ART.  131.  It  may  be  observed  here  that  each  of  the  United 
States  makes  its  own  laws  in  regard  to  negotiable  paper,  and 
probably  the  laws  of  no  two  States  agree  in  all  respects.  The 
laws  of  that  State  are  applied  in  which  the  paper  is  made 
payable,  though  it  be  drawn  in  another.  For  a  valuable 
comperid  upon  this  whole  subject  the  student  is  referred  to  a 
"  Manual  for  Notaries  Public,"  published  by  J.  Smith  Homans, 
New  York. 


DAYS     OF     GRACE.  187 

As  a  general  law  in  the  United  States  the  day  of  maturity 
for  all  negotiable  time-paper  does  not  come  till  three  days 
after  the  expiration  of  the  time  mentioned  in  the  instrument, 
except  when  the  time  is  limited  by  the  expression  "  without 
grace/'  These  days  are  called  days  of  grace,  but  they  give 
the  maker  no  special  advantage,  for  interest  is  allowed  on  those 
days  the  same  as  others,  and  no  presentment  need  be  made  till 
the  last  day  of  grace. 

If  the  last  day  of  grace  falls  on  Sunday,  or  any  legally  re- 
cognized holiday,  the  paper  is  payable  on  the  preceding  day. 

Bills  drawn  at  sight  are  sometimes  allowed  grace  and  some- 
times not.  The  statutes  of  different  States,  so  far  as  they 
exist,  do  not  agree,  and  in  the  absence  of  special  statutes  the 
custom  is  not  uniform.  In  New  York,  commercial  bills,  drawn 
at  sight,  are  payable  loitliout  grace,  and  all  paper  in  which 
either  the  maker,  drawer,  or  drawee  is  a  bank  or  banker,  is 
also  payable  without  grace. 

If  the  time  be  expressed  in  months,  calendar  months  are 
always  to  be  understood.  For  example,  three  months  from 
January  31,  without  grace,  would  be  April  30  ;  including 
grace,  May  3. 

If  the  time  be  expressed  in  days,  the  time  of  maturity  may 
be  found  by  taking  the  remaining  number  of  days  in  the  month 
of  the  date,  and  as  many  days  of  the  following  months  sepa- 
rately as  will  equal  the  given  number  of  days  plus  three.  The 
number  of  days  in  the  last  month  will  be  the  date  of  the  month 
on  which  the  paper  matures. 

For  example,  a  note  dated  August  20,  1858,  payable  ninety 
days  from  date,  would  mature  November  21,  1858. 

Solution.— 1 1  +  30  +  31  +  21 = 93. 

Or,  to  the  day  of  the  date  add  the  time  of  the  note  plus 
three,  from  which  subtract  consecutively  the  number  of  days 
of  each  following  month,  beginning  with  the  month  of  the 
date,  until  the  remainder  be  smaller  than  the  number  of  days 
in  the  next  month.  The  remainder  will  be  the  date  of  ma- 
turity. 

Solution.— 20  +  93=113,  and  113-31-30-31=21. 


188  DISCOUNTING     NOTES. 

Or,  if  the  time  be  30,  60,  or  90  days,  call  each  30  days  a 
calendar  month,  and  correct  by  subtracting  1  for  each  month 
passed  over  containing  31  days,  and  adding  1  or  2,  according 
as  it  is  a  leap  year  or  not,  if  the  last  day  of  February  be  in- 
cluded. 

Ttyus,  90  days  from  January  10,  1856,  would  be,  counting 
three  calendar  months,  April  13,  including  grace. 

Now,  from  13  subtract  1  for  January  and  1  for  March,  and 
add  1  for  February,  and  we  have  April  12,  for  the  result.  The 
last  rule  is  convenient  for  bank  paper,  which  usually  runs  30, 
60,  or  90  days. 

It  is  evident  from  the  above  rules  that  the  day  of  the  date 
should  be  excluded  from  the  calculation. 

The  following  fact  may  be  worth  remembering  by  those 
who  get  "  accommodations"  at  bank. 

A  paper  having  60  days  to  run  PROOF. 

will  mature  on  the  same  day  of  33  '==  7  x    5  —  2 

the  Aveek  as  that  on  which  it  was  63  =  7  x    9 

made.     Having  30  days  to  run,  it  =  7  ) 

will  mature  2  days  earlier  in  the  week,  and  having  90  days 
to  run  will  mature  2  days  later  in  the  week. 


DISCOUNTING     NOTES. 

ART.  132.  In  negotiating  promissory  notes  and  time-bills 
of  exchange  their  estimated  value  depends  upon  three  con- 
siderations, viz. 

1st.  The  responsibility  and  promptness  of  the  maker. 

2d.  The  relative  value  of  the  currency,  used  in  the  pur- 
chase, compared  with  that  of  the  payment  of  the  obligation  at 
maturity. 

3d.  The  market  rate  of  interest. 

The  range  of  the  first  consideration  is  from  A  No.  1  to 
worthless. 

The  range  of  the  second,  in  the  United  States,  is  generally 
within  2$. 


DISCOUNTING     NOTES.  189 

The  range  of  the  third  may  be  said  to  be  between  3  and 
20^  per  annum. 

In  view  of  the  first,  a  man  may  make  a  bad  bargain  in 
buying  a  note  having  sixty  days  to  run,  if  he  pay  for  it  but  10 
cents  on  a  dollar.  The  United  States  may  perhaps  borrow 
money  at  4$  per  annum,  when  individual  States  would  have 
to  pay  5  or  6$,  and  railroad  companies  10  or  15/c.  A  cor- 
responding difference  is  found  in  promissory  notes  made  by  in- 
dividuals and  business  firms. 

The  purchase  of  a  draft  on  New  York,  payable  in  coin, 
with  Illinois  paper  currency,  which  is  convertible  into  coin  at 
a  cost,  say,  of  1^,  will  illustrate  the  force  of  the  second  con- 
sideration. 

In  regard  to  the  third,  the  market,  or  ruling  rate  of  interest, 
depends  mainly  upon  the  rate  of  profit  with  which  capital  can 
otherwise  be  employed.  New  countries,  rapidly  developing, 
furnish  profitable  investments,  and  therefore  sustain  a  high 
rate  of  interest.  Sudden  expansions  and  contractions  of  cur- 
rency temporarily  affect  the  rate,  causing  it  to  fall  with  the 
expansion  and  rise  with  the  contraction,  but  a  continued  in- 
crease in  the  supply  of  money  stimulates  prices,  awakens 
enterprise,  and  increases  the  profits  in  business  and  specula- 
tion, thereby  raising  the  rate  of  interest  proportionably. 

The  rate  of  interest  does  not  express  the  value  of  money, 
but  only  the  value  of  the  use  of  it  for  a  limited  time,  or  rather, 
it  expfesses  the  value  of  the  use  of  the  capital  or  credit  mea- 
sured by  money.  Money,  from  its  nature,  is  always  cheap 
when  prices  are  dear,  and  vice  versa  ;  for  as  money  measures 
the  value  of  other  commodities,  so  the  comparative  price  of 
the  standard  articles  of  commerce  meacures  the  relative  value 
of  money.  Generally,  when  money  is  cheap,  interest  is  high. 
For  many  years  money  has  been  cheaper  in  the  United  States 
than  in  England,  but  during  the  whole  time  the  rate  of  in- 
terest has  ruled  higher.  Ifi  the  early  history  of  California 
money  was  exceedingly  cheap,  but  the  rate  of  interest  remark- 
ably high.  The  current  rate  of  interest  is  also  made  higher 
from  the  effect  of  unwise  usury  laws,  and  laws  under  which 


190  BANK     DISCOUNT. 

the  collection  of  valid  claims  can  bo  enforced  only  after  a  pro- 
tracted, uncertain,  and  expensive  prosecution. 

There  are  many  other  causes  that  occasion  remarkable 
fluctuations  in  the  market  rate  of  interest,  as  war,  commercial 
revulsions,  &c.  Unlimited  confidence  in  business  encourages 
a  high  rate  of  interest,  while  excessive  caution  and  distrust 
cause  it  to  decline. 

As  a  general  rule,  the  market  rate  of  interest,  like  the  price 
of  exchange,  is  not  subject  to  arbitrary  control,  but  is  the  re- 
sultant of  sundry  contributing  causes  ;  and  whatever  legisla- 
tion is  necessary  should  be  expended  on  the  cause  rather  than 
on  the  effect. 


BANK     DISCOUNT. 

AKT.  133.  The  banks  of  the  United  States  are  usually  re- 
stricted by  charter  in  their  rates  of  discount,  but  being  allowed, 
in  the  interior,  to  deal  in  time-drafts  or  bills  on  New  York, 
payable  in  coin,  and  being  allowed  frequently  to  pay  out  paper 
currency  of  less  value  than  coin  in  purchasing  such  drafts, 
they  are  enabled  by  this  and  other  means  to  realize  more  than 
the  nominal,  legally  restricted  rate  of  interest.  It  is  not  pro- 
posed in  this  work  to  discuss  the  policy  of  bank  charters  with 
special  privileges  and  special  restrictions,  nor  any  other  ques- 
tion of  policy,  but  merely  to  furnish  to  the  student  and  in- 
experienced business  man  the  fundamental  principles  upon 
which  money  and  negotiable  paper  do  rest  and  should  rest. 

It  may,  however,  be  taken  for  granted,  that  although 
banks,  railroad  companies,  &c.,  may  have  been  established  for 
"  the  accommodation  of  the  people/'  yet  so  long  as  they  are 
controlled  by  human  nature,  and  the  profits  go  into  the  pockets 
of  individuals,  corporations  no  more  than  individuals  can  be 
expected  to  furnish  "accommodations"  without  their  being 
paid  for.  As  a  general  rule,  a  business  man  may  expect  ac- 
commodations from  a  bank  only  so  far  as  he  makes  it  for  the 
interest  of  the  bank  to  grant  them. 


BANK     DISCOUNT.  191 

The  interest  which  is  charged  on  notes  discounted  at  a 
bank  is  generally  paid  in  advance,  and  is  computed  upon  the 
amount  due  on  the  note  at  maturity.  The  difference  between 
the  interest  and  face  of  the  note  is  the  proceeds,  which  is  re- 
ceived by  the  customer. 

Thus  the  proceeds  of  a  note  for  $2000,  having  63  days  to 
run,  including  grace,  would  be,  at  6^  interest,  $2000— §21  = 
$1979. 

If  "business  paper,"  drawing  interest,  is  discounted,  the 
amount  due  at  maturity,  including  interest,  is  taken  as  the  face 
of  the  note  upon  which  the  bank  discount  is  computed.  It 
will  be  observed  that  bank  discount  exceeds  the  "tru-e  dis- 
count," as  heretofore  explained ;  for  while  the  latter  is  the 
interest  on  the  present  worth  or  principal,  the  former  is  the 
interest  on  the  amount  of  principal  and  interest,  and  the  ex- 
cess is  equal  to  the  interest  on  the  true  discount  for  the  given 
time.  The  ratio  of  this  excess  will  also  increase  as  the  time  is 
lengthened,  -so  that,  other  considerations  remaining  the  same, 
the  longer  the  time  the  more  profit  to  the  bank.  If  the  note 
run  16 1  years,  the  bank  discount,  at  6$,  would  absorb  the 
whole  note,  and  the  proceeds  would  be  nothing.  Frequent  re- 
newals, so  far  as  the  matter  of  interest  is  concerned,  are  un- 
favorable to  the  bank.  The  reason  for  the  custom  among 
banks  of  discounting  only  "  short  paper,"  as  it  is  called,  is  two- 
fold. 

First,  A  large  portion  of  the  capital  invested  in  discounts 
is  based  upon  deposits,  which  are  subject  to  "  call,"  and  their 
own  "circulation,"  which  must  be  redeemed  on  presentation. 
In  case  of  unusual  demands  for  redemption,  or  withdrawal  of 
deposits,  the  early  maturity  of  Bills  Discounted  is  their  main 
reliance. 

Secondly,  The  risk  arising  from  the  varying  circumstances 
of  the  makers  and  indorsers  is  lessened  by  shortening  the  time. 

If,  however,  bills  of  exchange  are  discounted,  payable  in  a 
better  currency  than  that  used  in  the  discount,  or  for  which  a 
charge  is  made  for  collection,  the  shorter  the  time  the  greater 
the  pecuniary  profit. 


192     BANKERS'  ACCOUNT  CURRENT. 

In  considering  the  percentage  of  profit  in  "  bank  discount" 
with  frequent  renewals,  there  is  a  partial  offset  in  favor  of  the 
banker  by  his  being  able  to  compound  the  interest  at  each  re- 
newal. But  this  advantage  is  very  small  if  we  consider  its 
effect  for  one  year  only  (See  Note,  page  118),  at  which  time  sim- 
ple interest,  if  paid,  may  also  be  compounded  by  re-loaning. 

Comparing  simple  interest  with  "  bank  discount/'  includ- 
ing the  advantage  from  compounding  the  interest,  we  obtain 
the  following  result : 

Bank  discount  at  6^  on  paper, 

Renewed  once  in  12  mos.,  is  equivalent  to  6.383^  simple  interest. 
"       6         "  "     6.281^  " 

"  "      4        "  "  6.248#  " 

"  "       3         "  "  6.232^  " 

ic  ie      2         "  "  6.216$  " 

"  "      1         "  "  6.200^ 

"  every  instant  "  6.182^  " 

From  the  above  we  see  that  the  excess  of  bank  discount 
over  true  discount,  as  affecting  the  rate  of  interest  received, 
when  the  time  is  less  than  a  year,  can  be  but  trifling,  being  for 
§fo  always  less  than 


BANKERS'  ACCOUNT  CURRENT. 

ART.  134.  -Bankers  frequently  receive  and  pay  interest  on 
the  account  current  with  their  correspondents  and  depositors, 
paying  interest  on  the  deposits  and  receiving  interest  on  the 
over-drafts.  A  settlement  occurs  once  in  3,  6,  or  12  months, 
as  custom  or  special  agreement  may  dictate,  at  which  time  the 
balance  of  interest  is  entered  to  the  debit  or  credit  of  the  ac- 
count as  the  case  may  be,  after  which  it  draws  interest  the 
same  as  other  items  in  the  account.  The  principle  involved  in 
this  kind  of  interest  account  forms  the  basis  of  the  "MERCAN- 
TILE RULE"  in  Partial  Payments,  as  given  in  this  work. 

The  process  of  computing  the  interest  on  such  accounts  is 
made  easy  by  the  use  of  the  following 

RULE. — Divide  the  sum  of  all  the  daily  balances  by  6  and 


BANKERS'  ACCOUNT  CURRENT. 


193 


the  quotient,  after  pointing  three  places  for  decimals,  will  be 
the  interest  required. 

fiemark. — It  is  evident  that  each  daily  balance  draws  in- 
terest one  day.  The  interest,  then,  of  the  sum  of  daily  balances 
for  one  day  is  all  that  is  required. 

Note  1st. — If  the  daily  balance  remains  the  same  for  several 
days,  instead  of  setting  down  the  amount  as  many  times  as 
there  are  days,  use  the  product  of  the  balance  into  the  num- 
ber of  days. 

Note  2d. — If  the  balances  are  sometimes  debit  and  some- 
times credit,  take  the  difference  between  their  sums  before 
dividing. 

Note  3d. — The  above  rule  gives  the  interest  at  6$.  To 
find  the  interest  at  4.%  divide  by  9  instead  of  6.  For  3^,  divide 
by  12.  In  general,  the  divisor  for  any  rate  may  be  found  by 
dividing  36  by  the  rate.  Or,  having  found  the  interest  at  6$, 
the  interest  for  any  other  rate  may  be  found  by  aliquot  parts. 

Note  4th. — If  a  different  rate  of  interest  is  to  be  charged 
on  the  over-drafts  or  debit  entries,  the  footings  of  the  daily 
balances  should  be  divided  by  their  appropriate  divisors  before 
subtraction. 

The  following  abbreviated  form  will  serve  to  illustrate  the 
foregoing  rule : 


Account  Current 

Daily  Balances. 

Total  Daily  Balances. 

1859 

Dr. 

Cr. 

Dr. 

Cr. 

Dr. 

Cr. 

July  1 

$500 

500 

500 

2 

$200 

100 

400 

400 

3 

75 

325x17 

—  — 

5525 

20 

500 

825  x  10 

— 

8250 

30 

1000 

175 

x   5 

=875 

Aug.  4 

375 

200x10 

2000 

14 

125 

250 

325x30 

9750 

Sept.  13 

125 

450  x  10 

—  • 

4500 

23 

1000 

1450  x   8 

= 

11600 

Int.  4.63 

42525 

Bal. 

1454.63 

875 

2854.63 

2854.63 

9) 

41.650 

Oct.  1 

By  Bal. 

$1454.63 

Int.  at  4% 

$4.63 

13 


194  TRIAL     BALANCES. 

RULES  FOB  DETECTING-  ERRORS  IN 
TRIAL  BALANCES 

ART.  135.  The  first  rule  of  the  book-keeper  should  be  to 
make  no  error,  but  as  all  are  fallible  a  few  suggestions  may 
not  come  amiss. 

1st.  If  the  error  is  found  to  be  in  one  figure  only  it  is 
probably  an  error,  of  footing  or  copying. 

2d.  If  it  involves  several  figures  it  may  have  arisen  from  the 
omission  of  an  entire  entry  or  the  entering  of  the  same  twice. 

3d.  If  it  be  divisible  by  2,  without  a  remainder,  it  may 
have  arisen  by  posting  an  item  to  the  wrong  side  of  the  account, 
in  which  case  the  item  would  be  half  of  the  apparent  error. 

4th.  If  the  error  be  divisible  by  9,  without  a  remainder,  it 
may  have  arisen  from  transposition,  three  cases  of  which  may 
be  easily  detected  by  rules  founded  on  the  peculiar  property 
of  the  number  9.  They  are — 

First.  When  two  figures  are  made  to  exchange  places  with 
each  other,  the  orders  in  notation  remaining  the  same :  e.  g.} 
372  made  to  read  327,  or  732,  or  273. 

Second.  When  two  or  more  figures  are  made  to  change  their 
places  in  notation,  their  arrangement  in  respect  to  each  other 
remaining  the  same :  e.  g.}  $4275  made  to  read  $42750,  or 
$42.75,  or  $427.50. 

Third.  When  two  significant  figures  are  made  to  change 
position  both  with  respect  to  themselves  and  also  the  orders 
of  notation  :  e.  g.,  $14  made  to  read  $0.41. 

To  detect  the  first  and  second  cases  of  transposition  divide 
the  amount  of  the  error  in  the  trial  balance  successively  by 
9,  99,  999,  9999,  dc.,  so  far  as  possible  without  a  remainder, 
rejecting  all  ciphers  at  the  right  of  the  last  significant  figure  in 
the  error. 

The  quotients  that  contain  but  one  digit  figure  will  express 
the  difference  between  the  two  digit  figures  transposed,  which 
will  be  adjacent  to  each  other  if  the  divisor  contained  but  one 
9,  separated  by  one  other  figure' if  it  contained  two  9s,  by  two 
other  figures  if  it  contained  three  9s,  and  so  on. 


TRIAL     BALANCES. 


195 


Those  quotients,  which  contain  two  or  more  figures  will 
express  the  number  itself,  which  is  transposed  in  notation 
simply,  the  arrangement  of  the  significant  figures  remaining 
the  same.  In  either  case  the  order  of  the  last  significant 
figure  in  the  error  will  be  the  lowest  order  of  the  figures  trans- 
posed. The  orders  of  the  other  figures  can  be  easily  determined 
by  referring  to  the  error  and  applying  the  principles  of  no- 
tation. 

To  detect  the  third  case,  divide  the  error  in  the  balance  by 
as  many  9s  as  is  possible  so  as  to  give  only  a  single  figure  in 
the  quotient,  and  then  the  remainder  in  the  same  way,  reject- 
ing all  ciphers  at  the  right  of  the  last  significant  figure  in  both 
dividends,  after  which  there  should  be  no  remainder. 

The  first  quotient  will  be  the  figurS  filling  both  the  highest 
and  lowest  order  in  the  transposition  ;  the  second  quotient 
will  be  the  other  figure. 

Note. — If  the  error  of  the  trial-balance  be  not  divisible  by 
9  it  cannot  be  the  result  of  transposition  alone.  But  when- 
ever the  error  becomes  so  reduced  as  to  be  divisible  by  9  with- 
out a  remainder,  a  transposition  being  then  possible,  the  above 
tests  should  be  given. 

To  illustrate  the  application  of  the  foregoing  rules,  four 
examples  are  given  below,  each  one  representing  a  balance- 
sheet  taken  from  the  ledger,  but  erroneous,  from  the  fact  that 
the  footings  of  the  Dr.  and  Cr.  columns  do  not  agree. 


Dr. 

Or. 

Dr. 

Cr. 

Dr. 

Cr. 

Dr. 

Cr. 

25 

34 

184 

74 

100 

22 

184 

22 

100 

981 

24.50 

10.25 

320.60 

36.40 

23.50 

185 

87.50 

73 

30 

200.75 

400.90   20   | 

126 

71 

300 

90 

20.40 

80 

10 

31.20 

81.44 

137.80 

18.40 

92 

120 

110 

10.44 

10 

326 

323 

7 

93.50 

100 

50 

495 

800 

3.51 

6.44 

94 

12 

90.60!    33 

450 

200 

74.25 

100 

81.50 

310 

75    25 

100.16 

120.50 

353 

40 

144 

86.24 

201.75 

40 

30 

200.10 

25 

10 

63 

122.22 

8.25 

30 

20.10 

10 

350 

290 

922.40   11.84 

75 

333.92 

8 

49.50 

24 

35.99 

1,842.801,905.80 

855.25 

929.50 

1,945.20 

1,499.70 

1,570.70 

1.221.2.J 

63   , 

74.25' 

445.50 

349.47 

196  ,       TRIAL     BALANCES. 

The  "errors"  G3,  7425,  4455,  and  34947  being  each  divisi- 
ble by  9,  transposition  is  possible.  Taking  the  first  example, 
we  have  63-^-9=7.  As  this  is  the  only  division  we  can  per- 
form, we  conclude  the  transposition  can  occur  only  in  those 
amounts  where  the  digit  figures  expressing  the  units  and  tens 
of  dollars  differ  by  7.  In  the  Dr.  column  there  are  three  num- 
bers answering  these  conditions,  and  in  the  Cr.  column  two, 
viz. :  $18.40,  $7,  $81.50,  $981  and  $92.  The  transposition 
could  not  have  occurred  in  the  third  number  for  the  footing  is 
already  too  small.  If,  then,  either  of  the  other  numbers  had 
been  transposed  from  $81.40,  $70,  $918,  and  $29  respectively, 
the  error  is  accounted  for,  a  question  easily  settled  by  reference 
to  the  ledger.  In  the  second  example,  we  have  7425-^9=825 
and  7425-^99—75.  The  quotients  containing  two  or  more 
figures  in  the  transposition  must  be  in  notation  simply.  By 
reference  to  the  Dr.  and  Cr.  columns  it  will  be  observed  that 
these  quotients  occur  four  times  in  the  former  and  once  in  the 
latter,  viz. :  $0.75,  201.75,  $8.25,  $75,  and  $200.75.  The 
transposition  could  not  have  occurred  in  the  second  number 
without  displacing  other  significant  figures,  nor  in  the  fourth, 
because  the  Dr.  footing  is  already  too  small,  nor  in  the  fifth, 
because  the  Cr.  footing  is  already  too  large.  The  only  two 
numbers  to  be  compared,  therefore,  are  the  first  and  third, 
which,  perhaps,  should  have  been  $75  or  $82.50,  either  of 
which  would  account  for  the  error. 

In  the  third  example  we  have  4455 -r- 9 =495,  4455-r99 
=45.  Here  the  transposition  must  be  in  notation  simply, 
and  may  be  found  in  one  of  two  places  only,  viz. :  $495  and 
$450.' 

In  the  fourth  example  we  have  34947-^9=3883,  34947-f- 
99=353,  34947^9999=3,  with  a  remainder  495,  which  -^99 
=5.  We  omit  the  division  by  999,  because  the  remainder  is 
not  divisible  by  99  without  a  remainder.  For  the  same  rea- 
son we  omitted  it  in  the  third  example.  In  this  case  there 
could  be  no  transposition  in  the  notation  of  3883,  because  the 
number  does  not  occur.  There  may  have  been  a  transposition 
of  $353  from  $3.53,  or  the  figure  3  and  5  may  somewhere  have 


STOCKS     AND     BONDS.  197 

been  made  to  change  places  with  respect  to  themselves  and 
notation  also  ;  as,  when  $0.53  had  been  made  to  read  $350. 

Remark. — In  the  use  of  these  rules  in  practice,  not  only 
the  balances  of  the  ledger  accounts  as  they  appear  on  the 
balance  sheet  should  be  examined,  but  also  all  the  separate 
postings,  as  a  transposition  there  will  equally  affect  the  final 
balance. 


STOCKS    AND    BONDS. 

ART.  136.  Capital  is  a  term  applied  to  the  property  in- 
vested, by  an  individual  or  company,  in  trade,  manufactures, 
railroads,  banking,  &c.  The  capital  of  an  incorporated  com- 
pany is  generally  called  its  capital* stock,  and  is  divided  into 
equal  parts  of  convenient  size  called  shares :  the*  persons  own- 
ing one  or  more  of  these  shares  being  called  stockholders. 

The  management  of  such  companies  is  generally  vested  in 
officers  and  directors,  who  are  elected  by  the  stockholders,  each 
stockholder  being  entitled  to  as  many  votes  as  the  number  of 
shares  he  holds. 

It  not  unfrequently  happens  that  the  capital  stock  con- 
siderably exceeds  the  actual  capital  paid  in,  which  occurs  when 
it  is  made  payable  in  installments,  and  is  called  in  only  as  the 
wants  of  the  company  demand.  The  profits  which  are  distri- 
buted among  the  stockholders  are  called  dividends,  and  when 
"declared"  are  a  certain  per  cent,  of  the  par  value  of  the 
shares. 

Certificates  of  stock  are  issued  by  the  company,  signed  by 
the  proper  officers,  indicating  the  size  and  number  of  shares 
each  stockholder  is  entitled  to.  These  are  transferable,  and 
may  be  bought  and  sold  like  any  other  property. 

When  their  marketable  value  equals  their  nominal  value 
they  are  said  to  be  at  par.  When  they  sell  for  more  than 
their  nominal  value  or  face  they  are  above  par,  or  at  a  pre- 
mium ;  when  for  less,  they  are  beloio  par,  or  at  a  discount. 


198  STOCKS     AND     BONDS. 

Quotations  of  their  marketable  value  are  generally  made  by  a 
percentage  of  their  par  value. 

When  States,  cities,  railroad  companies,  and  other  corpora- 
tions borrow  large  amounts  of  money,  instead  of  giving  com- 
mon promissory  notes,  they  issue  bonds,  in  denominations  of 
convenient  size,  payable  at  a  specified  time,  with  interest  usu- 
ally payable  semi-annually. 

When  issued  by  governments  these  bonds  are  frequently 
called  government  stocks  or  State  stocks,  but  the  terms  should 
be  carefully  distinguished  from  the  capital  stock  of  business 
corporations. 

To  these  bonds  are  attached  what  are  called  coupons*,  each 
of  which  is  a  due  bill  for  the  interest  on  the  bond  to  which  it 
is  attached,  representing  the  amount  of  the  periodical  dividend 
or  interest,  and  the  time  of  payment,  which  coupons  are  sever- 
ally cut  off  and  presented  for  payment  as  they  become  due. 

These  bonds  and  coupons  are  signed  by  the  proper  officers, 
and,  like  certificates  of  capital  stock,  are  negotiable  by  delivery, 
being  made  payable  "  to  bearer."  The  loan  is  made  by  the 
sale  of  the  bonds,  with  coupons  attached,  but  they  are  rarely 
negotiated  at  par.  'Their  value  depends  upon  the  degree  of 
certainty  of  their  being  paid  at  maturity,  and  the  market  rate 
of  interest  compared  with  the  rate  drawn  by  the  bond. 

Treasury  notes  are  also  issued  by  the  United  States  govern- 
ment for  the  purpose  of  effecting  temporary  loans,  which  more 
nearly  resemble  bank  notes,  and  are  made  payable  with  inte- 
rest, but  without  coupoi 

Consols  is  a  term  abbreviated  from  the  expression  "con- 
solidated annuities,"  the  British  government  having  at  various 
times  borrowed  money  at  different  rates  of  interest,  and  pay- 
able at  different  times,  consolidated  the  stock  or  bonds  thus 
issued,  by  issuing  new  stock  drawing  interest  at  three  per  cent, 
per  annum,  payable  semi-annually,  and  redeemable  only  at  the 
option  of  the  government,  becoming  practically  perpetual  an- 
nuities. With  the  proceeds  of  this  the  old  stock  was  redeemed. 
The  quotations  of  these  three  per  cent,  perpetual  annuities  or 

*  Coupon,  pronounced  koo-pong'. 


STOCKS     AND     BONDS.  199 

consols,  indicate  pretty  accurately  the  state  of  the  money 
market,  as  they  form  a  staple  credit  and  become  a  standard 
for  reference. 

Examples. 

ART.  137.  1.  A  person  buys  25  shares,  par  value  $100 
each,  in  the  Illinois  Central  Kailroad,  at  a  discount  of  12$  per 
cent.  To  what  did  they  amount  ? 

2.  What  will  be  the  cost  of  $15,000  of  Ohio  State  Bonds, 
at  a  discount  of  2^$  ? 

3.  Bought  40  shares  ($100  each)  of  New  York  and  Erie 
Eailroad  stock,  at  a  discount  of  3$,  and  sold  the  same  at  a 
discount  of  37^$.     How  much  did  I  lose  in  the  transaction  ? 

4.  If  the  New  York  Central  Railroad  Company  declares  an 
annual  dividend  of  14$,  what  will  a  stockholder  receive  who 
owns  240  shares  ($100  each)  ? 

5.  How  many  shares  of  canal  stock,  of  $100  each,  at  14$ 
discount,  can  be  bought  for  $1020  ?     How  much  would  be 
gained  by  selling  them  at  33  \%  discount  ? 

6.  If  the  capital  stock  of  a  bank  be  $500,000,  what  amount 
is  necessary  to  declare  a  dividend  of  5|$  ? 

7.  A  person  owns  20  shares  ($100  each)  of  bank  stock, 
and  receives  a  dividend  of  $150  ;  what  was  the  rate  of  divi- 
dend ? 

8.  A  certain  stockholder  draws  $270  when  a  dividend  of 
9$  is  declared  ;  what  is  the  amount  of  his  stock  ? 

9.  Bought  stock  at  4  per  cent,  discount,  and  sold  the  same 
at  5$  premium,  and  gained  $450.     How  many  shares  of  $100 
each  were  transferred  ? 

10.  A  broker  paid  $9748.50  for  bank  stock,  at  a  discount 
of  3$.     How  many  shares  of  $50  each  did  he  purchase  ? 

11.  Which  is  the  better  investment,  railroad  stock  paying 
a  semi-annual  dividend  of  4$,  bought  at  a  discount  of  25$,  or 
money  loaned  at  10$  interest,  payable  annually  ? 

Ans.  Railroad  stock  by  f$,  besides  the  use,  each  year,  of 
one  semi-annual  dividend  for  six  months. 

12.  Bought  bank  stock,  paying  12$  dividend,  at  a  discount 
of  20$.     What  per  cent,  interest  did  the  investment  pay  ? 


200  STOCKS     AND     BONDS. 

13.  When  the  annual  dividend  of  railroad  stock  is  15$, 
and  the  interest  of  money  is  10$,  at  what  premium  ought  the 
railroad  stock  to  sell  ?  Ans.  50%. 

14.  At  what  per  cent,  discount  must  I  buy  bank  stock, 
paying  6$,  that  the  investment  may  pay  9$.         Ans.  33^$. 

15.  If  the  C.  &  E.  KR.  Co.  declare  a  dividend  of  15$  per 
annum,  what  is  the  value  of  its  stock,  money  being  worth  8$  ? 

16.  The  free  banking  law  of  New  York  requires  that  the 
stocks  deposited  with  the  superintendent,  as  security  for  bank- 
note circulation,  shall  be  made  equal  to  stock  producing  an 
interest  of  6$  per  annum.     What  amount  of  circulating  notes 
could  a  bank  receive  on  a  five  per  cent,  stock  ? 

Ans.  83 \%  of  the  par  value  of  the  stock. 
What  on  a  7$  stock  ?  Ans.  116|$. 

17.  In  January,  1848,  the  total  amount  of  British  consols 
was  £378,019,855.     What  was  the  amount  of  interest  paid  on 
them  semi-annually  ?  Ans.  £5,670,297f£. 

18.  The  debt  of  Great  Britain  and  Ireland,  in  round  num- 
bers, is  £780,000,000,  and  the  annual  revenue  £56,000,000. 
Supposing  the  annual  interest  to  average  3|$,  what  per  cent, 
of  the  revenue  is  needed  to  pay  the  interest  on  the  debt  ? 

19.  In  July,  1859,  forty-five  New  York  Fire  Insurance 
Companies  (out  of  fifty),  on  a  capital  of  $8,712,000,  divided 
among  the  stockholders,  as  a  semi-annual  dividend,  $679,950. 
Compared  with  railroad  stock  paying  5$  semi-annually,  which 
would  yield  the  greater  income,  railroad  stock  bought  at  65$ 
or  insurance  stock  at  par  ? 

20.  A  man  subscribed  $20,000  stock  in  a  mining  company, 
the  capital  stock  of  which  is  $500,000,  but  only  20$  paid  in.   A 
cash  dividend  of  2$  on  the  par  value  is  declared  and  a  dividend 
of  10$  to  be  credited  to  the  stockholders  as  an  installment  on 
their  unpaid  stock.     What  is  the  amount  of  cash  he  receives, 
and  what  is  the  balance  due  on  his  subscription  ? 

21.  I  buy  100  shares  of  $100  each  in  a  railroad  company, 
the  capital  stock  being  $3,000,000.     The  first  year  they  de- 
clare a  cash  dividend  of  10$.     The  second  year  they  increase 
their  stock  by  declaring  a  stock  dividend  of  10$.     The  third 


STOCKS     AND     BONDS.  201 

year  they  divide  among  their  stocknclclers  the  same  amount  as 
in  the  first  year.  What  would  be  the  per  cent,  of  the  last 
dividend  ?  Ans.  9T\  per  cent. 

How  much  more  would  they  need  to  declare  a  dividend 
of  10$,  the  same  as  in  the  first  year  ?  Ans.  $30,000. 

22.  If  the  paid  up  stock  in  a  railroad  company  be  worth 
100$,  and  a  stock  dividend  of  10$  be  made  to  the  stockholders, 
what  would  be  the  value  of  the  stock  after  the  dividend  ? 

Ans.  90} -J-  per  cent. 

23.  If  the  net  earnings  of  a  bank  with  $200,000  capital 
be  sufficient  to  pay  an  annual  dividend  of  10$,  and  reserve 
$4000  as  a  surplus  to  provide  for  future  losses,  and  it  pay 
6$  on  its  net  earnings  to  the  State  in  lieu  of  taxes,  what 
would  be  the  rate  of  taxation  on  its  capital  ? 

Ans.  TW  per  cent. 


NEW   RULE    FOB    FINDING-  THE   VALUE 
OF   A  BOND. 

ART.  138.  Most  of  the  problems  respecting  stocks  and 
bonds,  and  brokerage  in  money  and  exchange,  can  be  solved 
by  the  application  of  the  ordinary  principles  of  percentage; 
without  special  rules.  One  problem,  however,  not  unfre- 
quently  arises,  more  complicated,  to  the  solution  of  which  the 
attention  of  the  student  is  now  directed. 

To  find  the  present  value  of  a  bond  having  several  years  to  run, 
with  interest  payable  semi-annually,  in  order  to  realize  from 
the  dividends  and  final  payment  an  equivalent  to  a  given  rate 
per  cent,  per  annum  on  the  investment,  use  the  following 

RULE. — 1st.  Taking  a  single  dividend  or  semi-annual  in- 
terest on  the  bond  for  a  principal,  compute  the  simple  interest 
on  it  at  the  proposed  rate,  for  one-fourth  as  many  years  as 
would  be  the  product  of  the  number  of  semi-annual  dividends 
into  the  number  less  one.  To  this  interest  add  the  sum  of  the 
several  amounts  of  semi-annual  interest,  and  the  face  of  the 
bondj  setting  this  sum  down  for  a  DIVIDEND. 


202  STOCKS     AND     BONDS. 

2d.  Suppose  another  bond,  differing  from  the  given  bond 
only  in  its  rate  of  interest  being  the  same  as  the  proposed  rate 
for  investment.  Proceed  with  this  as  with  the  other,  and  use 
jthe  result  for  a  DIVISOR. 

The  quotient,  after  division,  wiU  express,  decimally,  the 
rate  per  cent,  of  the  par  value  equal  to  the  present  value. 

Ex.  1.  What  should  I  pay  for  a  bond  for  $1000  due  in  10 
years,  with  interest  at  6%,  payable  semi-annually,  in  order  to 
make  it  a  10$  investment  ? 

,  Solution. 

Interest  on  $25  at  10$.  for  AJIJIJL  years,          .         .      $237.50 
Total  amount  of  semi-annual  dividends  =$25  x  20=      500 

Face  of  the  bond, _1000_ 

Dividend, 1737.50 

Interest  on  $50  at  10$  for  AJ»  ju.  years,  .         .   "    475 

Total  amount  of  semi-annual  dividends  =$50  x  20=    1000 

Face  of  the  bond, 1000 

Divisor, ~2475~ 

$1737.50^$2475=.70202. 

$1000x.70202=$702.02,  the  present  value  of  the  bond. 

KEMABK. — A  strictly  accurate  solution  of  the  above  pro- 
blem requires  the  aid  of  logarithms,  and  the  operation  is  tedi- 
ous. The  above  rule  is  simple  and  brief,  and  gives  a  result 
sufficiently  approximate  for  all  practical  purposes.  The  ques- 
tion involves  compound  interest,  the  interest  on  the  investment 
being  supposed  to  be  compounded  annually,  while  the  interest 
on  the  dividends  is  compounded  at  the  proposed  rate  at  the 
end  of  each  year.  Though  annual  interest  gives  a  result  some- 
what less  than  compound  interest,  yet  if  two  problems  be 
wrought,  first  by  annual  interest  and  then  by  compound,  the 
ratio  between  the  results  by  the  first  operation  will  not  differ 
essentially  from  the  ratio  by  the  second.  This  principle  forms 
the  basis  of  the  rule  given  above.  The  work  of  computing  the 
"annual  interest,"  or  rather  semi-annual  interest,  is  much 
shortened  by  incorporating  in  the  rule  an  expression  for  the 
sum  of  the  arithmetical  series  of  years,  during  which  a  single 
dividend  would  draw  interest.  The  approximation  to  strict 


STOCK.S     AND     BONDS.  203 

accuracy  is  furthermore  increased  by  treating  the  supposed 
bond  or  investment  the  same  as  the  one  given,  so  far  as  that 
its  interest  should  be  payable  semi-annual ly  instead  of  annu- 
ally, as  proposed  in  the  conditions  of  the  problem. 

The  answer  given  to  the  above  example  in  PRICE'S  STOCK 
TABLES,  computed  by  logarithms,  is  70^  instead  of  70^,  as 
given  by  the  above*  rule. 

If  the  rate  per  cent,  to  be  realized  be  the  same  as  the  rate 
of  interest  on  the  bond,  the  present  value,  by  the  above  rule, 
would  be  the  par  value.  By  Price's  Stock  Tables  it  would  be 
at  a  premium  ;  if  7/c,  and  running  50  years,  the  premium  would 

be  1TVV  Per  cen*- 

Ex.  2.  Mosney  being  worth  10$  per  annum,  what  is  the 
present  value  of  a  7$  bond,  interest  payable  semi-annually, 
running  20  years  ?  Ans.  76 TW  per  cent. 

By  Price's  Stock  Tables.     "     75TVo        " 

Note. — As  the  ratio  only  is  sought,  any  convenient  amount 
may  be  assumed  for  the  face  of  the  bond. 

Ex.  3.  In  1813  the  United  States  government  borrowed 
§16,000,000,  selling  their  bonds  to  run  12  years,  at  6$  in- 
terest, payable  semi-annually,  at  12$  discount.  At  what  dis- 
count should  the  purchasers  have  taken  them,  to  realize  on 
their  investment  an  average  annual  interest  of  8$  ? 

Ans.  14ryo-<V$. 

KEMARK. — It  is  manifest  that,  if  a  corporation  sells  in  New 
York  its  bonds,  drawing  7$  interest,  for  less  than-par  value,  it  is 
borrowing  money  at  a  higher  rate  of  interest  than  the  legal  rate, 
and  the  contract  under  the  general  law  of  that  State,  regu- 
lating interest,  becomes  tainted  with  usury.  But  for  the  ac- 
commodation of  corporations,  and  the  security  of  capitalists  in- 
vesting in  such  bonds,  it  was  enacted  by  the  Legislature  of 
New  York,  in  1850,  that  "  no  corporation  shall  hereafter  in- 
terpose the  defense  of  usury  in  any  action/'  With  this  restric- 
tion upon  them,  corporations  can  negotiate  their  bonds  more 
readily  and  at  better  rates  than  without  such  restriction.  A 
large  class  of  individual  borrowers  desire  a  similar  legal  prohi- 
bition for  a  like  accommodation. 


204  EQUATION     OF     PAYMENTS. 


EQUATION     OF     PAYMENTS. 

ART.  139.  Equation  of  payments  is  the  process  of  finding 
the  mean  or  average  time  for  the  payment  of  several  sums  of 
money  due  at  different  dates.  The  mean  or  average  time 
sought  is  called  the  equated  time. 

The  common  methods  of  finding  the  equated  time  are  based 
upon  the  principle  that  money  kept  after  it  is  due  is  counter- 
balanced by  an  equal  sum  of  money  paid  the  same  length  of 
time  before  it  is  due. 

This  principle  obviously  depends  upon  another  which  may 
be  expressed  as  follows  :  The  payment  of  $100  down,  and 
$100  in  two  years  without  interest  is  equivalent  to  the  pay- 
ment of  $212  in  two  years,  without  interest,  the  rate  of  in- 
terest being  6  per  cent. ;  or  to  express  the  same  abstractly,  the 
use  of  any  sum  of  money  is  worth  its  interest  for  the  time  it  is 
used. 

ART.  140.  To  find  the  equated:  time  for  the  payment  of 
several  sums  of  morily  with  different  terms  of  credit. 

Ex.  1.  A  owes  B  $1200,  of  which  $300  is  due  in  4  months, 
$400  in  6  months  and  $500  in  12  months.  What  is  the 
equated  time  for  the  payment  of  the  whole  sum  ? 

FIRST     METHOD. 

300  x   4—1200  Explanation. — Suppose  the  sums 

400  x   6—2400  to  be  paid  respectively,  4  months, 

500x12=6000  6   months,   and  12   months  before 

1200        ~  ]9600  due.    The  amount  to  be  paid  will  be 

8  mos.  Ans.    $300 — its  discount  for  4  months  ; 

$400 — its  discount  for  6  ^months ; 

and  $500— its  discount  for  12  months.  The  interest  or  dis- 
count of  $300  for  4  months  equals  the  discount  of  $1  for  1200 
months  ;  the  discount  of  $400  for  6  months  equals  the  dis- 


EQUATION     OF     PAYMENTS.  205 

count  of  $1  for  2400  months  ;  the  discount  of  $500  for  12 
months  equals  the  discount  of  $1  for  6000  months  ;  or,  the 
discount  on  the  whole  sum  equals  the  discount  of  $1  for  1200 
+2400  +  6000—9600  months.  Now,  the  discount  of  $1  for 
9600  months  equals  the  discount  of  $1200  for  on*e-twelve  hun- 
dredths  of  9600  months =8  months,  the  equated  time. 

RULE. — Multiply  each  payment  or  debt  ~by  its  time  of  credit, 
and  divide  the  sum  of  the  PRODUCTS  by  the  sum  of  the  PAYMENTS. 

Note. — 1.  By  the  term  discount,  as  used  above,  is  meant 
mercantile  discount  or  simple  interest. 

2.  If  we  suppose  all  the  sums  to  be  paid  in  12  months,  the 
time  upon  which  the  last  debt  becomes  due,  the  amount  to  be 
paid  will  be  $300+ its  interest  for  8  months,  $400+ its  interest 
for  6  months,  and  $500,  or  $1200  + the  interest  of  $1  for  4800 
months.  It  is  plain  the  debts  will  be  cancelled  by  paying 
$1200  four  months  before  the  last  debt  is  due  ;  or,  which  is 
the  same  thing,  eight  months  after  the  first  debt  is  due. 

For  convenience  we  have  commenced  at  first  date  and  dis- 
counted. 

SECOND     METHOD. 

Discount  on  $300  for    4  months,  at  6$=$  6.00 

400  for    6          "          "  =   12.00 

500  for  12          "          "  =   30.00 

Discount  on  $1200  =$48.00 

$12= Discount  of  $1200  for  2  months 

6=       "  1200  for  1       " 

48-^6=8.        Ans.  8  months. 

Explanation. — The  interest  of  $1200,  or  the  sum  of  the 
payments,  being  $6  a  month,  A  is  entitled  to  the  use  of  $1200 
as  many  months  as  $6  is  contained  times  in  $48=8.  Hence, 
8  months  is  the  equated  time. 

RULE. — Find  the  interest  of  each  payment,  or  debt,  for  its 
term  of  credit,  and  divide  the  amount  of  interest  thus  found  by 
the  interest  of  the  sum  of  payments  for  one  month  or  one  day. 

Note. — As  the  result  will  be  the  same  for  any  rate  of  inte- 
rest, take  that  rate  which  is  most  convenient. 


206  EQUATION     OF     PAYMENTS. 

ART.  141.  That  the  equated  time  obtained  by  both  of  the 
above  methods  is  correct,  will  appear  from  the  following  proofs : 

First  Proof.— By  paying  the  $1200  at  the  close  of  8 
months  A  gains  the  use  of  $300  for  4  months=$6  interest, 
and  $400  for  2  months=$4  interest,  and  loses  the  use  of  $500 
for  4  months=$10  interest.  Hence,  A  gains  $6  +  $4=$10 
interest,  and  loses  $10  interest.  On  the  other  hand  B  loses  $6 
+ 4= $10  interest,  and  gains  $10  interest. 

Second  Proof. — If  neither  payment  should  be  made  till  the 
last  debt  is  due  A  would  then  owe  B  $300  + its  interest  for  8 
months=$300+$12=$312;  $400+its  interest  for  6  months 
=$400 +$12 =$412;  and  $500  without  interest:  that  is, 
A  would  owe  B  in  12  months  $312 +  $412 +  $500=  $1224. 
Now,  the  present  worth  of  $1224,  four  months  before  it  is  due, 
is  $1200.  Hence,  A's  paying  B  $1200  at  the  close  of  eight 
months  is  the  same  as  his  paying  him  $1224  in  12  months,  or 
$300  in  4  months,  $400  in  6  months,  and  $500  in  12  months. 

Third  Proof. — If  A  should  pay  each  debt  when  it  is  due, 
and  B  lend  the  money  received  to  C,  at  the  time  A's  last 
payment  is  due  C  would  owe  B  $24  interest.  If  A  should 
pay  the  sum  of  the  debts,  or  $1200,  at  the  equated  time  (8 
months),  and  B  lend  as  before,  he  would  also  receive  from  G 
$24  interest.  Hence,  the  amount  of  interest  is  the  same  in 
either  case,  and  8  months  is  an  equitable  time  for  the  payment 
of  the  debts. 

The  correctness  of  the  above  methods  is  called  in  question 
by  a  number  of  good  authors.  I  can  account  for  this  only 
by  the  well  known  fact  that  a  specious  error,  well  authenti- 
cated and  often  repeated,  sometimes  passes  current  among 
good  scholars,  without  being  submitted  to  the  rigid  test  of  ex- 
amination. The  following  is  the  common  method  of  demon- 
strating the  incorrectness  of  the  above  methods  of  finding  the 
equated  time  : 

"  If  I  owe  a  man  $200,  $100  of  which  is  now  due,  and  the 
other  hundred  in  two  years,  the  equated  time  is  not  one  year. 
For  in  deferring  the  payment  of  the  first  $100'  one  year  I  oughjb 
to  pay  the  amount  of  $100  for  the  time,  which  is  $106 ;  but 


EQUATION     OF     PAYMENTS.  207 

for  the  $100  which  I  pay  one  year  before  it  is  due,  I  ought 
to  pay  the  present  worth  of  $100,  which  is  §94.35f|;  and  $106 
+  §94. 35f£= $200.33 f£  ;  whereas  by  the  mercantile  method  I 
only  pay  $200." 

This  argument  is  fallacious.  For  if  I  ought  to  pay  the 
present  worth  ($94.33 1£)  of  the  $100,  I  pay  one  year  before 
it  is  due,  I  ought  not  to  pay  the  amount  ($106)  of  the  $100  I 
pay  one  year  after  it  is  due.  The  $6  interest  in  this  amount 
is  not  due  until  the  close  of  the  two  years.  I  ought  to  pay 
$100+ the  present  worth  of  $6  due  in  one  year,  which  is 
$5.66/3  ;  and  $100 + $5.66/3  +  $94.33fi= $200. 

The  mistake  is  in  considering  the  sums  of  money  payable 
at  different  times  as  separate  from  each  other ;  whereas,  by 
the  very  nature  of  the  problem  of  finding  a  common  time  of 
payment,  they  must  be  regarded  as  parts  of  the  same  contract. 
Suppose,  for  example,  I  buy  a  horse,  and  agree  to  pay  $100  in 
one  hour,  and  $100  in  two  years,  without  interest.  Failing  to 
pay  the  $100  due  in  one  hour  until  the  close  of  one  year,  which 
I  then  pay  luithout  interest,  how  much  must  I  pay  at  the  close 
of  the  second  year?  Evidently  $106  (if  the  legal  rate  is  6), 
since  I  paid  at  the  close  of  one  year  only  the  principal  ($100), 
leaving  the  interest  ($6)  unpaid,  which  cannot  draw  interest. 
Now,  in  finding  the  equated  time  for  the  payment  of  several 
debts  due  at  different  dates,  the  question  is  to  find  a  time  for 
the  payment  of  the  several  principals  loithout  interest.  Instead 
of  paying  the  amount  of  $100  in  the  problem  proposed,  the 
principal  alone  is  paid. 

The  following  is  given  by  these  authors  as  the  "  only  accu- 
rate rule :" 

.  Find  the  present  worth  of  each  of  the  given  amounts 
due;  then  find  in  what  time  the  sum  of  these  present  ivorths 
iv  iU  amount  to  the  sum  of  all  the  payments." 

The  inaccuracy  of  this  "  accurate  rule,"  tested  by  the  logic 
of  its  authors,  will  appear  from  the  following  : 

The  equated  time  for  the  payment  of  $200,  $100  of  which 
is  now  due,  and  the  other  $100  due  in  two  years,  as  found  by 
this  rule,  is  11.32075  months.  Now,  the  amount  of  $100  for 


208  EQUATION     OF     PAYMENTS. 

11.32075  months,  at  6  percent.,  is  $105.660387;  the  present 
worth  of  the  other  $100,  due  in  12.67925  months,  is  $94.03832, 
and  $105.660387+ 94.03832 =$199.698707,  whereas  it  ought 
be  $200. 

It  is  also  evident  that  the  equated  time,  as  found  by  this 
"  accurate"  rule,  will  not  be  the  same  for  all  rates  of  interest. 
At  50  per  cent,  the  equated  time  of  the  above  example  is  8 
months,  and  the  error,  by  the  above  test,  $8.33^  ;  at  100  per 
cent,  it  is  6  months,  with  an  error  of  $10. 

This  supposed  accurate  rule  is  based  upon  the  principle 
that  the  amount  to  be  paid  on  a  debt  due  at  a  future  date, 
without  interest,  at  any  time  previous  to  this  date,  is  the  pres- 
ent worth  of  the  debt  at  any  prior  date,  plus  the  interest  of  the 
present  worth  up  to  date  of  payment.  The  incorrectness  of 
this  principle  is  easily  shown.  Suppose  I  owe  a  man  $100, 
due  in  two  years,  without  interest  ;  how  much  ought  I  to  pay 
in  one  year  ? 

The  present  worth  of  $100,  due  in  two  years  (at  6  per 
cent:),  is  $89.2857,  and  the  interest  on  this  sum  for  one  year 
is  $5.3571 ;  hence  the  sum  to  be  paid  is  $89.2857 +  $5.3571  = 
$94.6428.  The  true  amount  to  be  paid,  however,  is  the  pres- 
ent worth  of  $100,  due  in  one  y^ar,  which  is  $94.339. 

In  finding  the  equated  time  for  the  payment  of  a  bill  of 
goods  or  of  an  account  current,  the  exact  number  of  days  be- 
tween the  different  dates  is  used.  The  pupil  may  commence 
with  the  first  dates  or  with  the  last.  In  commencing  with 
the  first  dates,  each  item,  except  the  first,  is  subject  to  dis- 
count;  if  the  last  date  is  taken,  each  item,  except  the  last, 
draws  interest.  ^ 

Ex.  2.  A  merchant  sold  goods  to  one  of  his  customers,  at 
different  dates,  as  by  the  statement  annexed.  What  is  the 
average  time  for  the  payment  of  the  same  ? 

June  16,  1858,  a  bill  amounting  to  $500,  no  credit. 

"     30,     "  "  "        220        " 

July   30,     "  "  "        300        " 

Aug.  15,     "  "  "        250        " 

Sept.    1,     "  «  "        112        « 

Oct.      1,     "  «  "        100        « 


EQUATION     OF     PAYMENTS.  209 

OPERATION   BY   FIRST   METHOD. 

days.  days, 

June  16,  1858,  §500  x   00= 

"  30,  '"  220  x  14=  3080 
July  30,  "  300  x  44=13200 
Aug.  15,  "  250  x  60=15000 
Sept.  1,  "  112  x  77=  8624 
Oct.  1,  "  100x107=10700  ^ 

1482  50604_34  days. 

4446J 
6144 
5928 

Counting  forward  34  days  from  June  16,  the  date  of  the 
first  bill,  we  have  July  20,  the  equated  time  for  the  payment 
of  the  above  bills. 

Note.  —  A  little  reflection  will  make  it  evident  that  the 
above  example  is  similar  to  one  requiring  the  equated  time  for 
the  payment  of  §500  cash  ;  §220  due  in  14  days  ;  $300  due 
in  44  days  ;  §250  due  in  60  days  ;  §112  due  in  77  days  ;  and 
§100  due  in  107  days.  The  average  date  of  purchase  of  several 
bills  is  found  in  the  same  manner. 

OPERATION   BY   SECOND    METHOD. 

days.      dis. 

June  16,  1853,  §500  for   00= 

"  30,  "  '  220  "  14=  J  .51* 
July  30,  "  300  "  44=  2.20 
Aug.  15,  "  250  "  60=  2.50 
Sept.  1,  "  112  "  77=  1.44 
Oct.  1,  "  100  "  107=  1.78 
§1482~  ~§8^3 

§14.82  dis.  for  60  days. 
.247      "        1  day. 
.247)  8.430  (34  Ana.  34  days. 


__ 
L020 

.988 
32 

Counting  forward  34  days  from  June  16,  we  have  July  2C, 
the  equated  time. 


210  EQUATION     OF     PAYMENTS. 

Note  — As  the  result  will  be  the  same  for  any  rate  of  inte- 
rest (discount),  it  is  generally  most  convenient  to  compute  the 
interest  at  6  per  cent.  When  the  time  is  in  days,  as  in  the 
second  example,  the  interest  is  readily  found  by  removing  the 
point,  or  separatrix,  two  places  to  the  left,  and  taking  such 
aliquot  parts  of  the  result  as  the  given  days  are  of  60  days. 

Suppose,  for  example,  we  wish  to  find  the  interest  of 
§230.60  for  39  days.  Since  39=30+6  +  3,  the  interest  for  39 
days  will  be  the  sum  of  |,  TV  and  ^  °f the  interest  for  60  days. 
Thus :  Interest  for  60  days  =$2.306 

"        "     30    "    (i)  =   1.153 
"        "      6     "  (TV)=     .231 
"      3     "  (¥v)=    jJ15 
"     39     "          =$1.50" 

Note. — 2.  If  the  equated  time  contains  a  fraction  greater 
than  i  add  1  to  the  number  of  days  ;  if  less  than  J  disregard  it 

Examples. 

3.  I  owe  $450,  due  in  6  months ;  $300,  due  in  8  months ; 
$125  due  in  10  months ;  and  $100,  due  in  12  months.     What 
is  the  equated  time  for  payment  ?  Ans.  7f  f  months. 

4.  Bought  a  farm  for  $3500  ;  |  of  it  is  to  be  paid  down,  \ 
of  it  in  8  months,  -}  in  12  months,  and  the  remainder  in  15 
months,  without  interest.     What  is  the  equated  time  for  the 
payment  of  the  whole  ?  Ans.  5£  months. 

5.  A  merchant  owes  a  bank  $1500,  of  which  $300  is  due 
in  30  days,  $250  in  45  days,  $350  in  60  days,  $450  in  80  days, 
and  $150  in  90  days.     What  is  the  equated  time  for  the  pay- 
ment of  the  whole  ?,  Ans.  61  days. 

6.  Bought  of  Ivison  &  Phinney  the  following  bills  of  goods : 

June   3,  1858,  a  bill  amounting  to  $300 
July    1,     "  "  "        220 

"    20,     "  "  "        400 

Aug.  15,     "  "  "        330 

Sept.  13,     "  240 

What  is  the  average  date  of  purchase  ?  Ans.  July  22. 

7.  A  merchant  has  charged  on  his  ledger  $120,  due  May 
15,  1858  ;  $90,  due  July  3,  1858  ;  $75,  due  Aug.  30,  1858  ; 

),  due  Sept.  10,  1858  ;  $160,  due  Oct.  18,  1858  ;  $150,  due 


EQUATION     OF     PAYMENTS.  211 

Dec.  20,  1858.     What  is  the  equated  time  for  the  payment  of 
these  accounts  ?  ^ns.  Sept.  10. 

ART.  142.  To  find  the  equated  time  for  the  payment  of 
several  sales,  made  at  different  dates,  and  for  different  terms 
of  credit. 

Ex.  1.  James  Russell  bought  of  Fink,  Hall  &  Co.,  several 
bills  of  goods,  as  below  stated  : 

April  3,  1858,  a  bill  of  $220,  on  3  months'  credit. 
May     1,      "          "  125,  on  5        " 

"     15,      "  "  200,  on  6 

June  24,      "          "  140,  on  8        "          " 

July     1,      "          "  190,  on  9        "          " 

What  is  the  equated  time  of  payment  ? 

Operation. 

days.  days. 

Due,  July    3,  1858,  $220  x  00= 
"    Oct.     1,     "        125  x   90=  11250 
"    Nov.  15,     "       200x135=27000 
"    Feb.  24,1859,    140x236=  33040 
"    April  1,     "        190x272=  51680 

875  )  122970(141  nearly. 

875 
3547 
3500 

470 

The  equated  time  for  the  payment  of  th*e  above  bills  is 
141  days  from  July  3,  which  is  Nov.  21. 

METHOD   BY   DISCOUNT. 

dis. 

Due,  July   3,  1858,  $220  for    00= 
"     Oct.     1,     "   '•  125  for    90=$  1.88 
"    Nov.  15,      "        200  for  135=    4.50 
"    Feb.  24,  1859,    140  for  236=    5.51 
"    April  1,      "   '     190  for  272=    8.61 


$875"  .1458  )§20.5000(141  days. 

8.75  1458 

G'o)-1458  5920 

5832 

880 

141  days  from  July  3,  is  Nov.  21,  the  equated  time  as  above. 

Explanation.— The  bill  of  $220  falls  due  3  months  from 
April  3,  which  is  July  3  ;  the  bill  of  $125  falls  due  5  months 


212  EQUATION     OF     PAYMENTS. 

from  May  1,  which  is  Oct.  1,  and  so  on  :  the  time  of  maturity 
of  each  bill  being  found  by  adding  its  term  of  credit  to  its  date 
of  purchase.  The  average  time  of  maturity  is  the  equated 
time  for  the  payment  of  the  bills. 

KULE. — First  find  the  MATURITY  of  each  bill  (or  the  time 
when  it  falls  due)  and  then  proceed  as  in  the  previous  case. 
The  equated  time  is  found  by  counting  fonoard  from  the  date 
of  the  first  amount  falling  due. 

Notes. — 1.  The  bill  having  the  earliest  date  does  not  always 
fall  due  first.  It  sonietimes  happens  that  the  term  of  credit 
of  the  first  bill  is  longer  than  that  of  the  succeeding  bills.  It 
is  most  convenient  to  arrange  the  statement  of  maturity  so 
that  the  bill  maturing  first  shall  stand  first. 

2.  The  equated  time  for  the  payment  of  several  bills  may 
be  found  by  commencing  at  the  last  date  and  finding  how  long 
each  bill  draws  interest.  Thus,  the  last  example  may  be 
equated  as  follows  : 

'  days.  days. 

Due,  April    1,  1859,  §190  x   00= 
"    Feb.   24,     "        140  x   36=     5040 
"    Nov.  15,  1858,    200x137=27400 
"     Oct.      1,     "   '     125x182=  22750 
"    July     2,     "       220x273=  60060 

875~         )115250(132  nearly. 
875_ 
2775 
2625 

1500 

The  equated  time  is  132  days  previous  to  April  1,  1859, 
which  is  Nov.  20,  1858.  The  difference  of  one  day  between 
the  results  of  the  two  methods  is  due  to  the  fractional  parts 
of  days  being  omitted. 

Examples. 

2.  T.  W.  Cook  &  Co.  sold  to  Murray  &  Co.  several  bills 
of  goods,  as  shown  in  the  statement  annexed.  What  is  the 
average  time  of  maturity  ? 

April  15,  1857,  a  bill  amounting  to  $450,  on  5  months'  credit. 
June  16,  "  '  "  560,  on  2 

July   31,     "  "  "        180,  on  6 

Sept.  19,     «  "  "        760,  on  5 


u  u 

a  a 

«  u 


Ans.  Nov.  19. 


EQUATION     OF     PAYMENTS.  213 

3.  Bought  goods  of  Smith  '&  Moore,  at  sundry  times,  and 
on  different  terms  of  credit,  as  follows  ? 

Dec.      18,  1857,  a  bill  of  $375.50,  on  6  months'  credit. 
Jan.      10,  1858,       "          290.60,  on  6      " 
March  13,     "  "          800.00,  on  8      " 

April   30,     «  "          650.80,  on  7      " 

June    15,      "  460.25,  on  4      " 

What  is  the  equated  time  for  the  payment  of  the  whole  ? 

Ans.  Oct.  8,  1858. 

4.  0.  Blake  &  Co.  sold  goods  to  J.  B.  Foster,  at  sundry 
times,  and  on  different  terms  of  credit,  as  follows  : 

Sept.    30, 1858,  a  bill  of  $  80.75,  on  4  months'  credit. 
Nov.      3,     "         "  150.00,  on  5      "          " 

Jan.       1, 1859,      "  30.80,  on  6       "          " 

March  10,     "          "  40.50,  on  5       "          " 

April  25,     "  60.30,  on  4      " 

How  much  will  balance  the  account  June  2,  1859  ? 

Ans.  $364.04. 

Note. — The  equated  time  for  the  payment  of  the  above  ac- 
count is  May  5, 1859  ;  hence  the  several  bills  above  are  equiva- 
lent to  a  bill  of  $362.35  due  May  5.  It  is  evident  that  the 
$362.35  should  draw  interest  from  May  5  to  June  2,  the  time 
of  settlement.  When  it  is  required  to  know  the  amount  due 
at  any  date  previous  to  the  equated  time,  the  present  worth* 
of  the  sum  of  the  several  bills  must  be  found. 

5.  A  merchant  sold  to  one  of  his  customers  several  bills  of 
goods,  as  follows  : 

May     9,  1857,  a  bill  of  $340  on  4  months'  credit. 
June    6,      "  "  400  on  3       " 

July    8,      "  "  345  on  5       "  " 

Aug.  30,      "          "          130  on  5       "  " 

Sept.  30,  240  on  6       "  " 

How  much  money  will  balance  the  account  Jan  1,  1858  ? 

Ans.  $1466.40. 

6.  J.  D.  Stuart  bought  of  Geo.  A.  Davis  &  Co.  several 
bills  of  goods,  as  follows  : 

*  The  mercantile  method  of  finding  the  present  worth  in  such  cases  is  to  de- 
duct interest  for  the  time. 


214  EQUATION     OF     PAYMENTS. 

March  3, 1850,  a  bill  of  $250,  on  3  months'  credit. 

April  15,     "   '       "  180,  on  4      " 

June  20,     "  "  325,  on  3       " 

Aug.  10,     "  "  80,  on  3       " 

Sept.     1,     "  100,  on  4      " 

What  is  the  equated  time  of  payment,  and  how  much  money 
would  balance  the  account  July  1,  1850  ? 

Ans.  Aug.  30  ;  $925.65. 

7.  Purchased  goods  of  a  merchant  at  sundry  times  and  on 
different  terms  of  credit,  as  follows  : 

Nov.  9,  1857,  a  bill  of  $  20.00  on  5  months'  credit. 
"  30,     "  "  50.60  on  3       " 

Dec.  31,     "  "  90.00  on  4      "  " 

Feb.  1,  1858,       "  120.00  on  3       " 

What  is  the  average  date  of  purchase,  and  what  the  average 
time  of  maturity  ?  Ans.  to  first  Jan.  4,  1858. 

8.  A  merchant  sold  goods  to  one  of  his  customers,  as  stated 
below : 

April   6,  1857,  a  bill  of  $450,  on  4  months'  credit. 

May  12,     "  "  600 

June  20,     ""         "  750 

Aug.    1,     "  "  300 

When  must  a  note  for  the  whole  be  made  payable  ? 

Note. — When  the  sales  have  the  same  term  of  credit,  as  in 
the  above  example,  it  is  most  convenient  to  find  first  the  aver- 
age date  of  purchase.  The  equated  time  of  payment  is  then 
readily  found  by  adding  the  common  term  of  credit  to  this 
average  date  of  purchase.  The  average  date  of  purchase  in  the 
above  example  is  54  days  from  April  6,  which  is  May  30 ;  the 
equated  time  of  payment  is  4  months  from  May  30,  which  is 
Sept.  30. 

The  days  of  grace  generally  allowed  may  be  added  to  the 
equated  time. 

9.  Sold  John  Smith,  on  a  credit  of  90  days,  the  following 

bills  of  goods : 

Jan.     10,  1858,  a  bill  of  $20. 

April,  12,      "  "  45. 

May    27,      «  "  60. 

June   30,      «  "  75. 

What  is  the  equated  time  of  payment  ?     Ans.  July  13, 1858. 


« 

tt  a 

a  a 


EQUATION     OF     PAYMENTS.  215 

10.  Purchased  goods  of  Stratton  &  Co,  at  different  dates, 
and  on  a  credit  of  6  months,  as  below  stated  : 

Oct.  12,  1858,  a  bill  of  $460  on  6  months'  credit. 

"    30,     "    •       "  95       "  " 

Dec.    1,     "  "          180      "  " 

"    25,     "  "          390      "  " 

Jan.  20,     "  "  410       "  " 

How  much  money  will  balance  the  account  July  1,  1858  ? 

Ans.  $1542.907. 

ART.  143.  To  find  what  extension  should  be  granted  to 
the  balance  of  a  debt,  partial  payments  having  been  made  be- 
fore the  debt  was  due. 

Ex.  A  owed  B  §1200,  due  in  6  months,  but  to  accomodate 
him  paid  $400  in  2  months.  When  ought  the  balance  to  be 
paid  ?  Ans.  in  8  months. 

Explanation. — Since  A  paid  B  $400  four  months  before  it 
was  due,  B,  at  the  close  of  the  6  months,  owed  A  the  interest 
of  $1  for  400x4  months^  1600  months.  To  balance  this  in- 
terest due  A,  he  can  keep  the  $800  unpaid  ¥£  0-  of  1600  months 
=2  months  after  the  debt  is  due. 

Ex.  2.  Singer  &  Morton  sold  Wm.  Williams,  June  10, 
1858,  goods  to  the  amount  of  §1300,  on  6  months  credit. 
Aug.  20,  Mr.  Williams  paid  $200  ;  Sept.  18,  $250 ;  Oct.  30, 
$350.  When,  in  equity,  ought  the  balance  to  be  paid  ? 

Operation. 

days. 

200  x  112  =  22400 

250  x     83  =  20750 

350  x     41  =  14350 

$800"  "~_57500 

57500^-500=115 

The  balance  ought  to  be  paid  115  days  from  Dec.  10,  1858, 
which  is  April  4,  1859. 

KULE. — Multiply  each  payment  by  the  time  it  was  paid 
before  due,  and  divide  the  sum  of  the  products  by  the  balance 
unpaid. 

3.  A  sold  B,  July  1,  1858,  goods  to  the  amount  of  $1500, 
on  a  credit  of  90  days.  Aug.  5,  B  paid  $400  ;  Sept.  3,  $600; 
Sept.  15,  $300.  When  ought  B  to  pay  the  balance. 

Ans.  April  26,  1859. 


216  EQUATION     OF     PAYMENTS. 

4.  A  merchant  sells  a  customer  to  the  amount  of  $600, 

1  of  which  is  to  be  paid  in  3  months,  |  in  4  months,  and  the 
balance  in  7  months.     The  customer  pays  1  down.     How  long 
may  he  keep,  in  equity,  the  remainder  ?       Ans.  7f  months. 

5.  A  owes  B  $600,  payable  in  6  months.     At  the  close  of 
3  months  he  wishes  to  make  a  payment  so  as  to  extend  the 
time  of  the  balance  to  one  year.     How  great  a  payment  must 
B  make  ?  Ans.  $400. 

Explanation. — B  wishes  to  pay  such  a  sum  of  money  three 
months  before  it  is  due,  as  will  extend  another  sum  6  months 
after  it  is  due.  It  is  evident  the  sum  paid  must  be  twice  as 
great  as  the  sum  extended.  Divide  $600  into  two  parts,  which 
shall  be  to  each  other  as  2  to  1. 

6.  A  owes  B  $1000,  payable  in  6  months.     At  the  close  of 

2  months  A  pays  B  $1200,  and  B  gives  A  his  note  for  the 
balance.     When  ought  the  note  to  be  dated  ? 

Ans.  24  months  back. 

Explanation. — Since  B  paid  A  $1200  four  months  before 
the  $1000  was  due,  A,  at  the  close  of  the  6  months,  owed  B 
the  interest  of  $1200  for  4  months,  or  $1  for  4800  months. 
It  is  evident  that  a  note  for  the  balance,  $1200— $1000= $200, 
must  be  dated  ^7  of  4800  months,  or  24  months  previous  to 
the  time  the  $1000  was  due. 

7.  July  10,  1858,  A  paid  B  $600 ;  Sept.  12,  1858,  B  paid 
A  $800.     When  ought  A  to  pay  the  balance  ? 

Explanation. — Sept.  12,  B  owed  A  $600+ its  interest  for 
64  days.  He  paid  A  $600 +  $200.  Hence,  A  is  entitled  to 
the  use  of  the  balance  ($200)  until  its  interest  equals  the  in- 
terest of  $600  for  64  days,  or  192  days.  192  days  from  Sept. 
12,  1858,  is  March  23,  1859. 

8.  July  10,  1858,  A  paid  B  $800 ;  Sept.  12,  1858,  B  paid 
A  $600.     What  should  be  the  date  of  a  note  for  the  bal- 
ance ? 

Explanation. — Sept.  12,  B  owed  A  $800  + its  interest  for 
64  days.  He  paid  A  but  $600.  Hence,  he  owes  A  the  bal- 


EQUATION      OF     ACCOUNTS. 


217 


ance  (§200)  and  the  interest  of  §800  for  64  days,  or  the  inte- 
rest of  $200  for  256  days.  A  note  for  the  balance  must  there- 
fore be  dated  256  days  previous  to  Sept.  12,  1858,  which  is 
Dec.  30,  1857. 

Jlemark. — The  above  eight  examples,  if  well  understood, 
will  aid  the  student  in  equating  accounts  which  contain  both 
debits  and  credits.. 


EQUATION     OF    ACCOUNTS. 

ART.  144.  Equation  of  accounts  (also  called  "Averaging 
of  Accounts/'  and  "  Compound  Equation  of  Payments")  is 
the  process  of  finding  the  equated  time  for  the  payment  of  the 
balance  of  an  account  that  contains  both  debits  and  credits. 

Since  the  debit  and  credit  sides  of  an  account  are  respect- 
ively equivalent  to  the  sum  of  their  several  items,  due  at  the 
equated  time  (See  Note,  page  213),  the  first  step  in  equating 
accounts  is  to  find  the  time  when  each  side  of  the  account  be- 
comes due. 

This  may  be  found  by  equating  each  side  of  the  account, 

without  any  reference  to  the  other,  commencing  either  at  the 
first  or  the  last  date  of  each,  or  by  using  the  first  or  last  date 
of  the  account  as  a  common  starting-point  for  both  sides. 

The  solution  of  the  following  example  will  sufficiently  illus- 
trate these  two  methods  of  equating  the  debit  and  credit  sides 
of  an  account. 

Note. — In  the  following  solution  we  have  commenced  at 
the  first  date  and  discounted  : 

Ex.  1. 
Dr.     Fisk,  Hull  &  Co.  in  account  with  Jas.  Russell.       Or. 


1838. 

\  Time  of  credit. 

1858. 

April   3 

ToMdse. 

$220      3  mo. 

July   1  By  Cash. 

$200 

May     1 

« 

12.3      5     " 

Oct.    3      " 

150 

"     15 

a 

200      6     " 

Dec.  20      " 

300 

June  24 

a 

140      8     " 

i 

July     1 

tt 

190      9     " 

i 

218 


EQUATION     OF     AC. COUNTS. 


FIRST 

Debits. 

Due, 
July    3,1853,   $220  X     00  = 

oct  i    «       125  x   90=11250 
NOV.  15,  »      200x135=27000 

Feb   84  1859        140  X  236  =  33040 

April  i,  •«      190x272=51680 

$875 


METHOD. 

Credits. 

Due. 
July    1,  1858,  $200  X     00= 

oct.   3,  «      150  x   94=14100 
Dec.  20,  »      300x172=51600 


$650 


) 65700 

101  ds. 

Credits  are  due  101  days  from 
July  1,  which  is  Oct.  10. 


) 122970 
141  ds. 

Debits  are  due  141  days 
from  July  3,  which  is  Nov.  21. 

The  above  account  thus  equated  will  stand  as  follows  : 
Dr.  Cr. 

Due,  Nov.  21,  1858,  $875.  I  Due,  Oct.  10,  1858,  $650. 

Or  tlius  : 

Debits. 

Due, 
July    3,  1858,  $220  X        2=       440 

oct.   i,  «      125  x   92=11500 
NOV.  15,  .«     200x137=27400 

Feb.  24, 1859,      140  X  238  =  33320 

April  i,  «      190x274=52060 

$875  . 


Credits. 

Due, 
July  1,  1853,  $200  X     00= 

oct.  3,  •«      150  x   94=14100 
Dec.  20,  ••      300x172=51600 
$650 


)124720 
T43  ds. 


) 65700 
101  ds. 
Credits  due  101  days  from 


July  1,  which  is  Oct.  10. 


Debits  due  143  days  from 
July  1,  which  is  Nov.  21. 

The  account  thus  equated  stands  as  before  : 

Dr.  Cr. 

Due,  Nov.  21,  $875.  |  Due,  Oct.  10,  $1650. 

Note.  —  In  the  above  operation,  we  start  from  the  earliest 
date  upon  which  any  item  of  either  side  of  the  account  be- 
comes due. 

The  next  step  is  to  find  when  the  balance  of  the  account, 
as  thus  equated,  becomes  due. 

Debits,  ....     $875  650 

Credits,      ...       650  42 

Balance,     .     .     .     $225 

Difference  in  time  42  days.  _ 

225)27300 

121  days. 


1300 


EQUATION     OF     ACCOUNTS.  219 

Or  thus,  by  Discount : 
$6.50  $4.55--.0375  (dis.  of  $225 

3~25  Dis.  for  30  days.  for  1  day) =121  days. 

1.30_     ^ 12     " 

$455T3is.  for  42  days. 

Balance  is  due,  121  days  from  Nov.  21,  1858,  which  is 
March  22,  1859. 

Explanation. — Assume  the  account  settled  Nov.  21,  the 
latest  date.  The  credit  side  of  the  account  has  heen  due  from 
Oct.  10  to  Nov.  12,  or  42  days.  Nov.  21,  the  credit  side  is 
equal  to  $650,  and  the  interest  of  the  same  42  days.  That  tjie 
debit  side  of  the  account  may  be  increased  by  an  equal  amount 
of  interest,  it  is  evident  that  the  balance  of  the  account  must 
remain  unpaid  121  days,  or  the  121  days  must  be  counted  for- 
ward from  Nov.  21. 

Or  thus  : 

The  above  account  may  be  stated  as  follows  :  Oct.  10, 
1858,  James  Kussell  paid  Fisk,  Hull  &  Co.  $650;  Nov.  21, 
1858,  Fisk,  Hull  &  Co.  paid  James  Kussell  $875.  Now,  since 
F.,  H.  &  Co.  had  the  use  of  $650  for  42  days,  J.  H.  is  entitled 
to  the  use  of  $225  (the  balance)  until  its  interest  equals  the 
interest  of  $650  for  42  days,  which  is  121  days.  121  days 
from  Nov.  21,  1858,  is  March  21,  1859. 


Pr 

Dr. 
Due  Nov.  21,     .     .      $875 
Int.  to  March  21,  1859,   17.65 

90/*. 

Or. 
Due,  Oct.  10,     .     .     $650 
Int.  to  March  21,  1859,  17.65 
Balance,    ....       '225. 

$892.65 

$892.65 

2.  Suppose  the  debit  and  credit  side  of  the  above  account, 
when  equated,  to  stand  as  follows  : 

Dr.  Or. 

Due,  Nov.  21, 1858,  $650.  |  Due,  Oct.  10,  1858,  $875. 


220  EQUATION     OF     ACCOUNTS. 

What  is  the  equated  time  for  the  payment  of  the  balance  ? 

Credits,      ....     $875  875 

Debits,       ....       650  _42 

Balance,     ....     $225  225)36750(163  days. 
Difference  in  time,  42  days.  225 

1425 

1350 

750 
675 


Balance  due  163  days  previous  to  Nov.  21,  1858,  which  is 
June  11,  1858. 

Explanation.  —  Suppose  the  account  settled  Nov.  21.  The 
credit  side  is  equal  to  $875,  and  its  interest  from  Oct.  10  to 
Nov.  21,  or  42  days.  That  the  debit  side  of  the  account  may 
be  increased  by  an  equal  amount  of  interest,  the  balance  of 
the  account  must  be  regarded  as  due  163  days  previous  to 
Nov.  21,  or  June  11. 

Or  tlius  : 

Oct.  10,  1858,  James  Kussell  paid  Fisk,  Hull  &  Co.  $875  ; 
Nov.  21,  1858,  F.,  H.  &  Co.  paid  J.  K.  $650.  Since  F.,  H.  & 
Co.  had  the  use  of  $875  for  42  days,  J.  H.  is  entitled  to  the 
interest  of  $225  (the  balance)  for  163  days.  Hence,  the  bal- 
ance must  be  regarded  as  due  163  days  previous  to  Nov.  21. 
The  simple  question  is  :  How  long  must  $225  be  on  interest 
to  equal  the  interest  of  $875  for  42  days  ? 

Note.  —  If  Fisk,  Hull  &  Co.  should  wish  to  give  their  note 
for  the  balance,  it  is  evident  the  note  must  be  dated  June  11, 
1858. 


First  find  the  equated  time  'for  each  side  of  the  account 
ivithout  any  reference  to  the  other.  Then  'multiply  the  side  of 
the  account  which  falls  due  FIRST  ~by  the  number  of  days  between 
the  dates  of  equated  time,  and  divide  the  product  by  the  balance 
of  the  account.  The  quotient  ivill  be  the  number  of  days  to  be 
counted  FORWARD  from  the  LATEST  DATE  ivhen  the  SMALLER 
side  of  the  account  falls  due  FIRST  ;  and  BACKWARD  when  the 
LARGER  side  falls  due  FIRST. 


EQUATION     OF     ACCOUNTS.  221 

NOTE. — Some  authors  give  the  following  rule : — Multiply  the  smaller  side  of 
the  account  by  the  number  of  days  between  the  dates  of  equated  time,  and  divide 
the  product  by  the  balance  of  the  account.  The  quotient  will  be  the  time  for  con- 
sideration. From  the  equated  date  of  the  larger  side,  count  FORWARD  when,  that 
side  becomes  due  last,  but  BACKWARD  when  it  becomes  due  first. 

ANOTHER   METHOD. 

ART.  145.  The  equated  time  for  the  payment  of  the  bal- 
ance of  an  account  may  be  found  directly  without  first  aver- 
aging the  debit  and  credit  items,  by  the  following  method  : 


Due, 


July    3, 1853,  $220  X        2=  440 

oct.  i,  «      125  x   92=  11500 

KOV.IS,  ••      200x137=  27400 

Feb.  24, 1853,    140x238=  33320 

Aprn  i,  «      190x274=  52060 


$875  124720 

650  65700 


Due, 


July  1,  1858,  $200  X        0= 

.      150  x   94=14100 
•      300x172=51600 
$650  65700 


262  days  from  July  1,  1858, 
is  March  21,  1858. 


§225  59020 

Explanation. — We  assume  July  1,  1858  (the  earliest  date 
upon  which  any  item  becomes  due),  as  the  time  upon  which 
all  the  items  of  the  account  becomes  due.  The  interest  of  the 
debit  items,  from  this  assumed  date  of  maturity  to  the  time 
they  respectively  become  due,  equals  the  interest  of  $1  for 
124720  days  ;  the  interest  of  the  credit  items  equals  the  inte- 
rest of  $1  for  65700  days.  Hence,  the  balance  of  interest  in 
favor  of  the  debit  side  equals  the  interest  of  $1  for  59020  days, 
or  $225  for  ^  of  59020  days=262  days.  Since  the  balance 
of  items  is  also  in  favor  of  the  debit  side,  it  is  evident  it  can 
remain  unpaid  262  days  without  interest,  or  will  become  due 
262  days  from  July  1,  1858,  which  is  March  21,  1859.  If  the 
balance  of  items  had  been  on  the  credit  side  it  would  have 
been  due  262  days  previous  to  July  1,  1858. 

HTJILIE. 

Assume  the  earliest  date  upon  which  any  item  of  the  ac- 
count becomes  due  to  be  the  time  of  maturity  for  all  the  items. 

Multiply  each  item  by  the  number  of  days  intervening  be- 
tween this  assumed  date  and  the  date  upon  ivhicli  it  becomes 
due,  and  find  the  sum  of  these  products  on  each  side  of  the  ac- 


222  EQUATION     OF     ACCOUNTS. 

count.  Then  divide  the  DIFFERENCE  betiveen  the  sums  of  the 
debit  and  credit  products  by  the  balance  of  the  account;  the 
quotient  ivill  be  the  time  for  consideration. 

When  the  difference  of  products  and  the  balance  of  the  ac- 
count fall  on  the  SAME  side  count  FORWARD  ;  when  on  OPPOSITE 
sides  count  BACKWARD. 

Note. — The  latest  date  may  be  used  as  a  starting-point. 
i 

Examples. 

3.  A  has  with  B  an  account,  which,  when  each  side  is 
equated,  stands  as  follows  : 

Dr.  Or. 

Due,  June  5,  $1285.  |  Due,  June  24,  $1080. 

What  is  the  equated  time  of  payment  for  the  balance  ? 

Ans.  Feb.  25. 

4.  C  has  with  D  an  account,  the  debit  and  credit  sides  of 
which,  when  equated,  are  as  follows  : 

Dr.  Or. 

Due,  Jan.  7,  $325  |  Due  Jan.  11,  $1090. 

What  must  be  the  date  of  a  note  for  the  balance  ? 

Ans.  Jan.  13. 

5.  What  is  the  equated  time  for  the  payment  of  the  bal- 
ance of  an  account,  which,  when  the  two  sides  are  equated, 
stands  as  follows : 

Dr.  Or. 

Due,  July  12,  $450.  |  Due,  Sept.  1,  $800. 

Ans.  Nov.  6. 

6.  At  what  time  will  the  balance  of  the  following  account 
commence  drawing  interest  ? 

Or.  Dr. 

Due,  Oct.  15,  $1260  |  Due,  Nov.  20,  $900. 

Ans.  July  17. 

7.  What  is  the  equated  time  for  the  payment  of  the  bal- 
ance of  the  following  account,  the  merchandise  items  having  a 
credit  of  4  mouths  ? 


EQUATION     OF     ACCOUNTS. 


223 


Dr.         E.  Bill  &  Co.  in  account  with  Orvil  Blake. 


Cr. 


1858. 

1859. 

. 

May     1 

To  Mdse.  $850 

70 

Jan.    1  By  Cash. 

?500 

00 

June    6 

it 

340 

75 

Jan.  19 

1C 

440 

00 

July     3 

a 

180 

25 

Feb.    1 

tt 

100 

00 

Aug.  13 

tt 

500 

00 

Feb.  15 

ft 

980 

00 

20         " 

340 

40 

30 

80 

00 

Ans.  808  days  back  of  Jan.  28,  1859. 

Note. — In  finding  the  equated  time,  when  the  cents  are  less 
than  50  reject  them  ;  when  more,  add  $1.  The  work  will  be 
sufficiently  accurate. 

8.  When  will  the  balance  of  the  following  account  com- 
mence drawing  interest,  allowing  that  each  item  was  due  from 
date  ?  What  will  balance  the  account  Oct.  1  ? 


Dr. 


A  in  account  with  B. 


Cr. 


1858. 

July  10 
"    30 

Aug.  30 
Sept.  9 
"    30 

To  Mdse. 
u 

a 
tt 
tt 

§120 
450 
380 
560 
400 

00 
00 
00 
00 

oo  ; 

1858.      | 

Aug.  20  By  Cash. 
Sept.  25  !  "    Mdse. 
Oct.      3   "     Cash. 

1 

$350 
250 
950 

00 
00 
00 

Ans.  to  first,  Dec.  12. 

Remark. — Since  the  balance  of  the  above  account  com- 
mences to  draw  interest  at  the  equated  time  of  the  account,  it 
is  evident  that  the  cash  value  of  this  balance,  at  any  date  sub- 
sequent to  the  equated  time  of  the  account,  may  be  found 
by  adding  to  the  balance  its  interest  up  to  date;  and  at  any 
date  previous  to  the  equated  time,  by  deducting  from  the  bal- 
ance its  interest  for  the  intervening  time.  By  mercantile  cus- 
tom interest  is  deducted  (as  in  the  last  case)  instead  of  finding 
the  true  present  worthy  when  money  is  paid  before  it  is  due. 

9.  When  will  the  balance  of  the  following  account  com- 
mence drawing  interest  ?  What  will  be  the  cash  value  of  the 
balance,  Jan.  1,  1859  ?  Credit  of  90  days  on  merchandise 
items. 


224 


CASH     BALANCE. 


Dr. 


B  in  account  with  C. 


Or. 


1858. 

\ 

1858. 

Aug.  18 

To  Mdse.  $  50|  00 

Oct.     7  By  Cash. 

$200 

00 

Sept.  15 

a 

140  00 

"     30 

a 

100 

00 

"     30 

" 

80  00 

Dec.    1 

n 

400 

00 

Oct.     8 

tt 

200  00 

Nov.    1 

a 

350  00 

u 

CASH    BALANCE. 

ART.  146.  When  an  account  current  is  settled  by  cash,  it 
is  not  necessary  to  find  the  equated  time  as  in  the  preceding 
article.  The  true  or  cash  balance  of  an  account  at  a  particu- 
lar date  may  be  found  directly  as  follows  : 

Ex.  1. 
Dr.     Dr.  Murray  &  Co.  in  account  with  Jones  &  Sons.     Or. 


1859. 

1859. 

April  10 

To  Mdse. 

§150 

April  12 

By  Cash. 

$250 

"     30 

a 

400 

May      1 

a 

180 

May    16 

it 

90 

June     7 

a 

400 

'•     24 

a 

100 

"     25 

tt 

564 

June     1 

a 

300 

"     10 

a 

340 

"    26 

it 

200 

What  will  be  the  true  balance  of  the  above  account  July 
1,  1859,  the  time  of  settlement,  allowing  that  each  item  draws 
interest  from  its  date,  at  6  per  cent.  ? 

Operation. 
Debits. 


.Lme,  Days. 

April  10,    $150x82=  12300 


30, 
May  16, 
"  24, 
June  1, 
"  10, 
"  26, 


62=  24800 
90x46=  4140 
100x38=  3800 
300x30=  9000 
340x21=  7140 
200  x  5=  1000 


§1580 


6)62180 
$ia364 


Due, 


Credits. 

April  12,  $250x80=20000 

May      1,  180x61=  10980 

June    7,  400x24=     9600 

"      25,  564  x   6=     3384 


$1394 


6)43964 
"7.327 


CASH     BALANCE.  225 


Sum  of  debit  items,    $1580 

"     credit    "  1394 

Balance  of  items,          $186 


Int.  of  debit  items,  $10.364 

"     credit     "          7.327 

Balance  of  interest,    $3.037 


True  balance,  July  1,  $186 +  $3.04= §189.04. 

Explanation  — Since  each  item  of  the  debit  side  of  the  ac- 
count was  on  interest  from  its  date  to  the  time  of  settlement, 
the  total  interest  of  the  several  debit  items  equals  the  interest 
of  $1  for  62180  days,  which  is  $10.364.  (The  interest  of  $1  for 
6  days  is  1  mill ;  hence,  the  interest  of  $1  for  62180  days  is 
found  by  dividing  62180  by  6,  and  pointing  off  three  decimal 
places.)  The  total  interest  of  the  several  credit  items  equals 
the  interest  of  $1  for  43964  days,  which  is  §7.327.  Now,  in- 
stead of  increasing  each  side  of  the  account  by  its  interest,  and 
then  finding  the  balance,  this  same  result  may  be  obtained  by 
finding  separately  the  balance  of  items  and  the  balance  of  in- 
terests. If  the  two  balances  fall  on  the  same  side  of  the  ac- 
count, it  is  evident  the  true  balance  will  be  their  sum  ;  if  on 
different  sides,  their  difference. 

METHOD      BY     INTEREST. 


Due,                                     Davs.            Int. 

April  10,  $150  for  82=f2.05 

"     30,     400  for  62=   4.133 
Mav    16,       90  for  46=     .69 
•  "     24,     100  for  38=     .634 
June     1,     300  for  30=   1.50 
"     10,     340  for  21=   1.19 
"     26,     200  for   5=     .17 

Due,                                       Days.            Int 

April  12,  $250  for  80=  $3.333 
May      1,     180  for  61=   1.83 
June     7,     400  for  24=   1.60 
•  "     25,     564  for    6=     .564 

$1394              $7.327 

$1580             $10.367 

Balance  of  items     =$1580    -$1394  =$186. 

"        of  interest=$10.367— $7.327=     $3.04. 
True  balance,     .     =$186      +$3.04  =$189.04 

Note. — The  "method  by  interest''  will  generally  be  found  most  convenient 
either  for  finding  the  equated  time  for  the  payment  of  the  balance  of  accounts,  or 
in  finding  the  cash  balance. 

The  above  account,  when  balanced  by  interest,  may  be 

presented  as  follows  : 

15 


226 


CASH     BALANCE. 


Dr.         Murray  &  Co.  in  account  with  Jones  &  Sons.     Cr. 


1589.    , 
April  10 
"     30 
May    16: 
"     24 
June     1 
'•     10 
26 
] 


To  Mdse. 


July 


bal.  by  int. 


Am't.      Da 

$150.0082 

400.00  62 

90.0046 

100.0038 

300.0030 

340.0021 

20000    5 

3.04 


$1583.04 


Int 
$2.05 

4.133 
.69 
.634 

1.50 

1.19 
.17 

$10367 


1853. 

April  12  By  Cash. 


July 


$250.00  U*. 
180.00  80 
400.00,6'- 
564.0024 

*  189.04    6 


$3.333 
1.83 
1.60 
.564 


$7.327 


$1583.04 


Errors  excepted.  Portsmouth,  July  1,  1859.  Jones  &  Sou. 

RULE. 

Multiply  each  item  of  the  account  by  the  number  of  days 
intervening  betiveen  the  date  on  ivhicli  it  becomes  due  and  the 
time  of  settlement.  Divide  the  sums  of  the  debit  and  credit 
products  respectively  by  6  :  the  quotient  will  be  the  interest  of 
the  two  sides  of  the  account,  at  6  per  cent.,  expressed  in  MILLS. 
Find  the  balance  of  items  and  also  the  balance  of  interests. 

When  the  two  balances  fall  on  the  SAME  side  of  the  account, 
the  cash  balance  will  be  their  SUM  ;  when  on  opposite  sides, 
their  DIFFERENCE. 

Or, 

Find  the  interest  of  each  item  from  the  date  on  ivhich  it 
becomes  due  to  the  time  of  settlement  The  difference  between 
the  sums  of  interests  on  the  debit  and  credit  sides  of  the  ac- 
count ivill  be  the  BALANCE  OF  INTEREST. 

When  the  balance  of  interest  falls  on  the  same  side  as  the 
balance  of  items,  the  cash  balance  will  be  their  SUM  ;  lohen  on 
opposite  sides,  their  DIFFERENCE. 

2.  The  following  account  was  settled  July  1, 1857.  What 
was  the  cash  balance,  interest  being  computed  on  each  item 
from  date  at  *l%  ? 

Dr.          James  Kehoe  in  account  with  J.  Smith.  Cr. 


1857.    | 

lint,  or 
Ds'  prods. 

1S5S. 

Ds. 

Int.  or 
prod& 

Jan.     7  To  bal.  of  acc't. 

$120.00 

April  1 

By  cash. 

$140.00 

"      15 

'  mdse. 

96.75 

"     30 

u          a 

50.00 

"      24 

'  bills  payable 

130.50 

May  20  "  order  on  T.S. 

140.00 

Feb.  27 

'  mdse. 

200.80 

"    31 

"  cash. 

450.00 

March  7 

<       <t 

80.00 

June  11 

"  Mdso.               500.00 

May  10 

«       ii 

300.00 

June    9 

u          « 

240.75 

Ans. 


ACCOUNT     OF     SALES. 


227 


3.  What  was  due  on  the  following  account,  Jan.  1,  1858, 
interest  6  per  cent.,  and  a  credit  of  90  days  being  allowed  on 
each  merchandise  item  ? 

Dr.          John  Scott  in  account  with  Geo.  Fields.          Cr. 


1557. 

Days. 

lot  or 

products. 

1857      j                                    j^'ys-    Int-or 
product 

July     3ToMdse.$104 

85 

Aug.  12  By  Mdse.  $300  00 

"       16        " 

340 

60 

"      25 

j.       n 

11680 

"       31 
Sept.  13;      " 

G7 
236 

80 

Sept.  15 
Oct.    13 

II             <( 

"  Cash. 

33975 
5000 

«      20 

9038 

Xov.    1 

u       K 

14875 

* 

"      27 

6084 

Oct.      l|      " 

36040 

Ans.  $307.492. 

4.  What  would  have  been  the  true  balance  of  the  above 
account  Jan.  1,  1858,  at  7  per  cent.,  no  credit  being  allowed 
on  merchandise  items  ?  Ans.  §316.563. 


ACCOUNT    OF    SALES. 

ART.  147.  An  account  of  sales  is  a  statement  of  the  quan- 
tity and  price  of  goods  sold,  the  charges  incurred  in  the  sales, 
and  the  net  proceeds,  which  a  commission  merchant  or  con- 
signee makes  to  his  employer  or  consignor. 

The  net  proceeds  is  the .  sum  to  which  the  employer  is  en- 
titled after  all  charges  are  deducted.  The  net  proceeds  are 
due  as  cash  at  the  equated  time  of  the  different  sales. 

The  following  examples  will  give  a  fuller  idea  of  an  ac- 
count of  sales. 

1.  Account  of  sales  of  grain  for  Fisk,  Cook  &  Co. 


Data 

Purchaser. 

Description. 

Bush.    Price. 

$ 

1858. 

Jan.     30  M.  B.  Gilbert/Wheat, 

white. 

250  §  .95 

237.50 

Feb.      3  Crest  &  Fisk.  Wheat, 

med. 

1000     .88 

880.00 

"      16  Wheeler&Co.  Corn. 

'2000     .55 

1100.00 

"     28  C.  A.  Davis.  Oats. 

1500      .371 

562.50 

March  20  T.  C.  Skinner.  Wheat, 

Kv.  white. 

750    1.00" 

750,00 

April     9  Talcott  &  Co.  Wheat, 

red. 

1450      .85 

1232.50 

"     28  J.B.Howard.  Corn. 

1300      .58 

754.00 

May      7T.  Bentoa 

1C 

450     .60 

270.00 

"      30  F.  Hart. 

Wheat, 

med. 

9551     .90 

859.50 

1           §6646.00 

228 


CASH     BALANCE. 


Charges. 

Commission  2|  per  cent,  on  $6646,   $166.15 

May  30— Freight  on  955  bushels  wheat,     .          47.75 

Drayage  and  sacks,      .         .         .          51.00 

Advertising  in  "  Tribune/'          .  7.50 

,  V .   $272.40 
Net  proceeds  to  credit  of  F.  C.  &  Co.,  $6373.60 

Errors  excepted. 
New*  York,  June  1,  1858.  SMITH  &  JONES. 

2.  Sales  544  barrels  flour,  for  account  of  P.  Rhodes  &  Son, 
Navarre,  0.,  by  Bryant  &  Stratton,  Cleveland,  0. 


1858. 

S  «?'S   • 

2    2    •  g  ,OT 

o  *  £§ 
SHps 

0 

a 
£ 

July  2 

a      tt 

"     5 

June  15 

P.  Anderson. 

it 

Morgan  &  Co. 

Charges  : 
Trans.     Boat 
"  Kent." 
Less  am't  de 
on  boat. 

Storage. 
Insurance. 
Commission 

Proceeds  to 

400 

125 

19 

=544bls. 
damage 

cash,  Jul 

§30 

505 

750 

3,320 
95 
937 

50 

4,352 

50 

05 

45 

400125  19 

400 
due 

on 
ere 

125 

ted 

43 

dit 

i 

19 

for 

5250 
as 

16 

3 

*\% 

y  10 

8704 

10 
7704 
1632 
1088 
10881 

213 
4,139 

1858. 
1 

4,35250 

Cleveland,  0., 
July  12,  1858. 


(Signed)      BRYANT  &  STEATTON. 


3.  What  will  be  due  P.  Rhodes  &  Son  on  the  above  ac- 
count January  1,  1859  ? 


CASH     BALANCE. 


229 


4.    Sales,  100  barrels  linseed  oil,  for  account  of  Robert 
Miller,  Warren,  0.,  by  Bryant  &  Stratton,  Cleveland,  0. 


1855. 

Bis. 

Gala. 

May  14 

a  it 

"  15 

"  18 

"  13 

Cash. 
Gaylord  &  Co. 

Cash. 
it 

Charges  : 
Tr.,  Boat  Cuyahoga. 
Storage. 
Fire  Insurance. 
Cooperage. 
Com.  on  365S28 

Net  proceeds  due  as 

10 
30 
5 
55 

403 
1,200 
201i 
2,200" 

95 
92 
95 
90 

37s 

8$ 

M* 

z& 

18, 

38285 
l,104j 
19143 
1,980! 

3,658 

148 
3,5~09 

28 

60 
68 

100 
100 

cas 

4,0041 
h  May 

37 

8 
9 
2 
91 

50 

14 

50 
46 

1855. 

Cleveland,  0.,  (Signed)       BRYANT  &  STRATTOX. 

May  24,   1855. 

5.    Sales  of  provisions  for  account  of  M.  Fisher  &  Co., 
Cincinnati,  0.,  by  James  &  Co.,  St.  Paul,  Min. 


1353. 

Boxs 
& 
kegs 

Bis. 

Pieces. 

Pounds. 

• 

Feb.  7 

"Wheeler  &  Co. 

29 

Sams,  plain. 

1450 

8£ 

"   22 

M 

42 

"       sugar  cured. 

2300 

10i* 

Mar.  6 

U 

18 

Shoulders,  plain. 

846 

7^ 

"     15  Altrara  &  Co. 

|25 

Mess  pork,  Xo.  2. 

IP 

Apr.  3  E.  Miller. 

15 

i 

Kegs  butter.  "W.  R. 

840 

w 

a       a 

ISO 

[Cheese. 

4200 

6^ 

"    10  Wheeler  &  Co. 

150  Bacon  sides. 

2432 

7ic 

May  2  Altram  &  Co. 

15 

Mess  pork,  Xo.  2. 

16* 

"      5.G-eo.  Singer. 

37  Shoulders  (city). 

2512 

7ff 

I 

0.3 

40 

2761 

14.580 

Charges. 

Feb.    1— Freight  of  13,040,  at  70$.  per  100. 
April  2^       "  5,040,  "  68c.       " 

Storage,  ff».     Cooperage,  3-°r=SSO. 
Fire  Insurance,  at    ±%  on  §. 
Commissions,      "  2|^  "   §. 

Net  proceeds  as  cash,  due 

St.  Paul's,  Minnesota,  JANES  &  Co. 

May  15,  1858. 


230  ANNUITIES.. 


ANNUITIES. 

ART.  148.  An  Annuity  (L.  annus,  a  year)  is  a  fixed  sum 
of  money  payable  annually,  or  at  the  end  of  equal  periods  of 
time,  to  continue  for  a  given  number  of  years,  for  life,  or  for- 
ever. 

A  certain  Annuity,  or  an  Annuity  certain,  is  one  that  is 
payable  for  a  definite  length  of  time. 

A  contingent  Annuity  is  one  that  is  payable  for  an  uncer- 
tain length  of  time  ;  as  during  the  life  of  one  or  more  persons. 

A  perpetual  Annuity,  or  an  Annuity  in  perpetuity,  is  one 
that  continues  forever. 

A  deferred  Annuity,  or  an  Annuity  in  reversion  (whether 
certain,  contingent,  or  perpetual)  is  one  that  begins  at  a  future 
time  ;  as  at  the  death  of  a  certain  person. 

An  immediate  Annuity,  or  an  Annuity  in  possession,  is  one 
that  begins  at  once. 

An  Annuity  forborne,  or  in  arrears,  is  one  whose  pay- 
ments have  not  been  made  when  due. 

The  amount,  or  final  value,  of  an  annuity  is  the  sum  of 
the  amounts  of  all  its  payments,  at  compound  interest,  from 
the  time  each  is  due,  to  the  end  of  the  annuity. 

The  present  value  of  an  annuity,  at  compound  interest,  is 
the  sum  of  the  present  values  of  all  its  payments  ;  or  the  pres- 
ent worth  of  its  final  value.  The  present  value,  put  out  at 
compound  interest,  will  amount,  at  the  time  of  the  expiration 
of  the  annuity,  to  its  final  value. 

The  subject  of  annuities  is  one  of  great  practical  import- 
ance in  the  affairs  of  life.  Its  principal  applications  are  leases, 
life-estates,  rents,  dowers,  reversions,  life-insurance,  etc.  The 
problems  are  readily  solved  by  means  of  tables. which  give  the 
present  and  final  values  of  $1  for  a  given  number  of  years  at 
the  ordinary  rates  of  interest.  A  complete  discussion  of  the  > 
principles  upon  which  these  tables  are  computed  would  require 
too  much  space. 


ANNUITIES. 


231 


ART.  149.  A  TABLE, 

Showing  the  present  value,  and  also  the  amount,  or  final  value, 
of  an  annuity  of  $1,  for  any  number  of  years  not  exceeding 
fifty : 


Present  value  of  an  Annuity  of  $1. 


Final  value  of  an  Annuity  of  $1. 


«?  4  per  cent. 

* 

|        ! 
5  per  cent.  6  per  cent  7  per  cent 

1 

4  per  cent 

5  per  cent. 

6  per  cent. 

7  per  cent. 

1  0.961  533 

0.952  331 

0.943  39G 

0.934  579 

1 

1  1.000  000 

1.000  000 

1.000  000 

1.000  000 

2  1.S36  095 

1  1.S59  410 

!  1.833  893 

1.803  017 

2 

2.040  000 

2.050  000 

2  060  000 

2.070  000 

0  2.775  091 

i  2.723  248 

2.673  012 

2.624  314 

3 

8.121  600 

8.152  500  3.183  5-iO 

3.214  900 

1  4l  &629  895 

3.545  951 

8.465  10G  3.387  207 

4 

4.246  464 

4.310  125  4.374  616 

4.439  943 

5  4.451  822 

4.329  477 

4212  364 

:  4.100  195 

5 

5.416  323 

5.525  631 

5.G37  093 

5.750  739 

6  5.242  137 

5.075  692 

4.917  824 

4.766  537 

G 

6.632  975 

6.801  913 

6.975  319 

7.153  291 

7  6.602  055 

5.736  373 

5.5S2  381 

5.339  286 

7 

7.893  294 

8.142  003 

8.393  833 

8.654  021 

8  6.732  745 

6.463  213 

6.209  744 

5971  295 

S 

9.214  226 

9.549  109 

9.897  468 

10.259  803 

9  7.435  33-2 

7.107  822 

6.301  692 

6.515  223  9 

10.582  795 

11.020  564 

11.491  316 

11.977  989 

10  8.110  893 

7.721  735 

7.360  087 

7.023  577 

10 

12.006  1C7 

12.577  803 

13.180  795 

13.816  448 

11  8.760  477 

8.306  414 

7.886  875 

7.498  669 

11 

13.483  851 

14.206  737 

14.971  64=3 

15.783  599 

12  91385  074 

8.863  252 

8.383  844 

7.942  671 

12 

15.025  805 

15.917  127 

16.869  941 

17.888  451 

13  9.935  613 

9.393  573 

8.852  683 

8.357  635 

Ifl 

16.626  808 

17.712  933 

13.S82  138 

20.140  643 

14  li'.~>63  12-3 

9  893  641  1  9.294  984 

8.745  452  14 

18.291  911 

10.593  632 

21.015  066 

22.550  483 

15  11.113  357  10.379  60S 

0.712  249 

9.107  898 

15 

20.023  5SS 

21.573  564 

23.275  970 

25.129  022 

16  11.652  296:10.837  770*10.105  895 

9.446  632 

16 

21.824  5S1 

23.657  492 

25.670  528 

27.888  054 

17  12.105  G69 

11.274  066 

10.477  260 

9.763  206 

17 

23.697  512  !  25.840  366  28.212  830 

30.840  217 

IS  12.659  297 

11.6*9  537 

10.327  603  10.059  070'  18 

25.645  413!  28.132  335  30  905  653 

33.999  033 

1!)  13.103  039 

12.0S5  321 

11.153  116 

10.335  578 

10 

27.671  229 

80.539  004 

33.759  992 

37.378  965 

20  13.590  826 

12.4C2  210  11.469  421 

10.593  997 

20 

29.778  079 

33.065  954 

36.785  591 

40.995  492 

21  14.029  16) 

12.821  153  11.764  077  10.835  527 

21 

31.969  202 

35.719  252 

39.992  727  i  44.865  177 

22  14.451  115 

13.163  Ot.3 

12.041  532 

11.061  24! 

•22 

34.247  970 

38.505  214 

43.392  200 

49.005  739 

23  14.856  842 

13.433  514  12.303  379  11.272  187 

23 

36.617  839 

41.430  475 

46.995  823 

53.436  141 

•24  -15246  963 
25  15.622  030 

13.798  642  12.550  3."  8  11.469  8:34 
14.093  945  12.783  856  11.653  5S3 

24  39.1182  604 
25|  41.645  908 

44.501  909 
47.727  099 

50  815  577 
54.864  512 

5^.176  671 
63.249  030 

26  15.982  7G9 

14.275  1S5 

13.003  166 

11.825  779 

•26 

44.311  745 

51.113  454 

59.156  383 

63.676  470 

27  16329  586  14.643  034 

13.210  534  11.986  709 

27 

47.084  214 

54.6J6  126 

G0.7r.->  76  i 

74.483  823 

28  16.653  063 

14.893  127 

13.406  164 

12.137  111 

23 

49.967  583 

53.402  533 

68.528  112 

80.697  691 

29  16.933  715 

15.141  074 

13  590  721 

12.277  674 

•20 

52.966  236 

62.322  712 

73.630  793 

87.346  529 

30  17.292  033 

15.372  451 

13.764  831 

12.409  041 

80 

56.084  9:38 

66.403  843 

79  058  136 

84.460  786 

31  17.533  494 

15592  811 

13.929  086 

12.531  814 

•31 

59.328  335 

70.76D  790 

84.801  677 

102.073  041 

32  17.873  552 

15.302  66V 

14.034  040  12.646  555 

02 

62.701  469 

75.293  829 

90.839  77.5 

110.218  154 

33  18.147  646 

16.002  549 

14.230  200 

12.753  790 

88 

66.209  527 

80.168  771 

97.343  105 

118.933  425 

34  13.411  108 

16.192  204 

14.368  141 

12.854  0;;9 

04 

69.857  909 

85.066  950  104.183  "55 

128.258  765 

35  13.664  613^6.374  194  14.493  246 

12.947  672 

05 

73.652  225 

90.320  307  111.434  780  1G8.236  878 

36  13.908  232 

16.545  852 

14620  987 

13.C35  208 

86 

77.598814  95.  S3G  323  119.120  867 

148.913  460 

37  19.142  579 

167il  2>7 

14.736  780 

13.117  017 

37 

81.702  24GI101.623  109  127.263  119 

1C0.337  400  : 

3S  19367  864 

16.S67  t93 

14846  019 

13.193  473 

OS 

85.970  336:K'7.709  646185.904  206 

172.561  020 

39  19.534  48i 

17.017  041 

14.949  075 

13.264  928 

89 

90.4U9  150  114.095  0'23  145.058  45:. 

135.640  292 

4C  19.7U2  774 

17.159  CS6  15.046  207 

13.331  709 

40 

95.025  51C,  120.709  774  154.701  966  199.635  112 

| 

41  19993  052 

17.294  363  15.133  016  13.394  120 

41 

90.826  536  127.839  763  165.047  CSi 

214.609  570 

42  ifl.lSS  627 

17423  203 

15.224  543 

13.4:2  440 

42 

104.  SI  9  593  155.201  751  175.950  645 

230.632  24ti 

43  -'0.370  795 

17.545  912 

15.306  173 

13506  962 

4:; 

110.012  382  142.993  3391187.507  577 

247.776  406 

44  2)543  841 

17.662  773 

15.883  1-2 

13.557  90S 

44 

115.412  877  151.143  006  109.753  <>02 

266.120  851 

45  20.72J  04)  17.774  070  15.455  832  13.605  522 

45|l21.029  392  159.7uO  156  212.743  51-!  285.749  311 

j 

46  20  8?4  654 

17.880  C67  15.524  870  13.650  020 

46  126.870  563  163  685  164  226.508  125  S06.751  763 

47.21.043  906 

17.931  016 

15.689  028 

13.691  60S 

47 

132.945  890  173.119  422  241.098  612 

829.224  386 

4321  10.3  131 

18.077  153 

15.650  027 

13.730  474 

48 

139.263  206  183.025  893  '256564  529 

a53.270  093 

4921.341  472 

IS.  163  72215.707  572 

13.766  799 

49  145.833  734  193.426  6fi3  272.953  401  378.999  OOf 

5021432  135 

18.255  925  15.761  861 

13.800  746 

50  152.667  034  209.347  976  290.335  9.)5  406.523  929 

232  ANNUITIES. 

ART.  150.  To  find  the  amount,  or  final  value,  of  an  annuity 
certain,  at  compound  interest,  in  arrears,  or  forborne. 

Ex.  1.  Suppose  a  rental  of  $500  a  year  to  remain  unpaid  8 
years  ;  what  is  the  amount  due,  at  5  per  cent,  compound  in- 
terest ?  Ans.  $47745.545. 

Operation. 
$9.549109,  amount  of  $1  for  8  years.     (See  Table). 

500 
$47.745.545 ;          "      $500     < 

RULE. — Multiply  the  amount,  or  final  value,  of  an  annuity 
of  $1,  for  the  given  rate  and  time,  by  the  given  annuity. 

Note. — When  the  annuity  draws  simple  interest,  the 
amount  is  found  as  in  annual  interest. 

Ex.  2.  Find  the  final  value  of  an  annuity  of  §150,  running 
12  years  at  4  per  cent,  compound  interest. 

Ans.  $2253.87+. 

Ex.  3.  An  annuity  of  $200  has  been  in  arrears  15  years  ; 
what  is  the  amount  due,  at  6  per  cent,  compound  interest  ? 

Ans.  $4655.194. 

ART.  151.   To  find  the  present  value  of  an  annuity  certain. 

Ex.  1.  What  is  the  present  value  of  an  annuity  of  $120, 
to  continue  25  years,  at  6  per  cent.  ?  Ans.  $1534. 

Operation. 

$12.783356,  present  value  of  $1.     (See  Table.) 

120 

$1534.002720  "  §120. 

EULE. — Multiply  the  present  value  of  $1,  as  an  annuity 
for  the  given  rate  and  time,  ly  the  given  annuity. 

Note. — Since  the  present  value  of  an  annuity  is  the  present 
worth  of  its  amount,  or  final  value,  the  present  value  of  an 
annuity  may  also  be  found  by  first  finding  the  amount,  and 
then  the  present  worth  of  this  amount. 

Ex.  2.  What  is  the  present  value  of  an  annuity  of  §650,  to 
continue  15  years,  at  5  per  cent.  ?  Ans.  $6746.7777. 


ANNUITIES.  233 

Ex.  3.  What  is  the  present  worth  of  a  leasehold  of  $1200, 
payable  annually  for  50  years,  at  6  per  cent.  ? 

Ans.  $18914.23. 

Ex.  4.  A  widow  is  entitled  to  $140  a  year,  payable  semi- 
annua]Jy,  for  18  years  ;  what  is  the  present  value  of  her  inte- 
rest, at  10  per  cent  compound  interest  ?  Ans.  $1158.80. 

Ex.  5.  I  wish  to  purchase  an  annuity  which  shall  secure  to 
my  ward,  at  4  per  cent,  compound  interest,  $250  a  year  for 
14  years.  What  must  I  deposit  in  the  annuity  office  ? 

.   Ans.  $2640.78. 

ART.  152.  To  find  the  present  value  of  a  perpetuity. 

Ex.  1.  What  is  the  present  value  of  a  perpetual  leasehold 
of  $1200  a  year,  at  5  per  cent.  ?  Ans.  $24000. 

Operation. 
$1200.00-^.05=:$24000,  present  value. 

Explanation. — The  present  value  must  evidently  be  a  prin- 
cipal which  yields  an  annual  interest  of  $1200,  at  5  per  cent. 

KULE. — Divide  the  given  annuity  l>y  the  interest  of  $l,/or 
one  year. 

Ex.  2.  What  is  the  present  value  of  the  perpetual  lease 
of  $4800  a  year,  at  8  per  cent,  interest  ?  Ans.  $60000. 

Ex.  3.  What  is  the  present  value  of  a  perpetual  leasehold 
of  $1600  a  year,  payable  semi-annually,  at  6  per  cent,  interest 
per  annum  ?  Ans.  $27066|. 

Suggestion. — When  an  annuity  is  payable  semi-annually, 
or  quarterly,  interest  must  be  allowed  on  the  half-yearLy  or 
quarterly  payments  to  the  close  of  the  year.  The  annuity  in 
the  last  example  is  $1624. 

Ex.  4.  The  ground  rent  of  an  estate  yields  an  annual  in- 
come of  §2400,  payable  quarterly,  at  4  per  cent,  per  annum. 
What  is  the  value  of  the  estate  ?  Ans.  $60900. 

ART.  153.  To  find  the  present  value  of  a  certain  annuity 
in  reversion. 

Ex.  1.  What  is  the  present  value  of  an  annuity  of  $250, 
deferred  12  years  and  to  continue  10  years,  allowing  6  per 
cent,  compound  interest  ?  Ans.  $914.43+. 


234  ANNUITIES. 

Operation. 

$12.041582— present  worth  of  $1  for  22  yrs. 
_8.383844  "  12  yrs. 

"$37657738  "  "          10  yrs.  deferred  12  yrs. 

250 

$914.434500  "  $250  "  " 

Explanation. — The  present  worth  of  an  annuity  of  $1  for 
22  years  must  be  equal  to  its  present  worth  for  12  years,  plus 
its  present  worth  for  the  10  succeeding  years.  Hence  the  pres- 
ent worth  of  an  annuity  of  $  1  for  10  years  deferred  12  years 
must  equal  its  present  worth  for  22  years,  minus  its  present 
worth  for  12  years.  The  present  worth  of  $250  is  evidently 
250  times  the  present  worth  of  $1. 

EULE, — Find  from  tlie  table  the  present  value  of  an  annu- 
ity of  $1,  commencing  at  once  and  continuing  till  the  TEKMI- 
NATION  of  the  annuity,  and  also  till  the  reversion  COMMENCES. 
Multiply  the  differences  of  these  present  values  ~by  the  given 
annuity. 

Note. — If  the  annuity  is  perpetual,  the  present  worth  of 
$1,  commencing  at  once,  is  found  according  to  the  last  article. 

Ex.  2.  What  is  the  present  value  of  a  leasehold  of  $1800, 
deferred  10  years  and  to  run  20  years,  at  5  per  cent,  compound 
interest  ?  Ans.  $13771.2888. 

Ex.  3.  A  lease,  whose  rental  is  $1000  a  year,  is  left  to  two 
sons.  The  elder  is  to  receive  the  rent  for  9  years  and  the 
youngest  for  the  12.  years  succeeding.  What  is  the  present 
value  of  each  son's  interest,  allowing  6  per  cent,  compound  in- 
terest ?  Ans.  to  last,  $4962.385. 

Ex.  4.  What  is  the  present  value  of  a  perpetuity  of  $900, 
to  commence  in  30  years,  allowing  4  per  cent,  compound  inte- 
rest ?  Ans.  $6937.17. 

ART.  154.  To  find  the  annuity,  the  present  or  final  value, 
time  and  rate  being  given. 

Ex.  1.  An  annuity  running  20  years,  at  7  per  cent,  com- 
pound interest,  is  worth  $15,000  ;  what  is  the  annuity  ? 

Ans.  $1415.89. 


.ANNUITIES.  235 

Operation. 
$•15000  -^-  $10.593997  =  1415.89. 

Explanation. — Since  §10.593997,  at  7  per  cent,  compound 
interest  for  20  years,  yields  an  annuity  of  $1,  $15000  will 
yield  an  annuity  equal  to  $15000-^10.593997. 

RULE. — Divide  the  present  or  final  value  of  the  given  annu- 
ity by  the  present  or  final  value  of  an  annuity  of  $1,  for  the 
given  rate  and  time. 

Ex.  2.  An  annuity  in  arrears  for  8  years,  at  5  per  cent, 
compound  interest,  amounts  to  $47745.545  ;  what,  is  the  an- 
nuity ?  Ans.  $500. 

Ex.  3.  A  yearly  pension,  unpaid  for  12  years,  at  6  per 
cent,  compound  interest,  amounted  to  §1591.7127  ;  what  was 
the  pension  ?  Ans.  $100. 

Ex.  4.  The  present  value  of  a  lease,  running  25  years,  at  6 
per  cent,  compound  interest,  is  $15340.037 ;  what  is  the  an- 
nual income  ?  Ans.  §1200. 


CONTINGENT     ANNUITIES. 

ART.  155.  When  the  annuity  is  to  cease  with  the  life  of  a 
certain  person  or  persons,  it  becomes  necessary  to  ascertain  the 
probability  of  the  person  or  persons,  upon  the  continuance  of 
whose  life  the  annuity  depends,  surviving  a  given  period.  The 
measure  of  this  probability  is  called  Expectation  of  Life,  and 
has  already  been  noticed  under  Life  Insurance. 

In  computing  contingent  annuities,  the  expectation  of  life 
of  the  person  or  persons  named,  as  shown  in  Bills  of  Mortality, 
is  taken  as  the  time  of  the  annuity.  It  can  then  be  computed 
as  an  annuity  certain. 

A  table,  showing  the  present  value  of  an  annuity  of  $1,  to 
continue  during  the  life  of  an  individual,  is  called  a  Table  of 
Life  Annuities. 

ART.  158.  To  find  the  present  value  of  a  life  annuity. 


ANNUITIES. 


Ex.  1.  What  is  the  present  value  of  a  life  pension  of  $150, 
the  age  of  the  pensionary  being  75  years  ;  interest,  5  per  cent.  ? 

Ans.  8748.35. 


Ans.  $748.35. 
Operation. 


$4.989 — value  of  annuity  of 
150 


$748.350  $150. 

KULE. — Multiply  the  present  value  of  a  life  annuity  o/"$l, 
as  shown  in  the  table,  by  the  given  annuity. 

Ex.  2.  Suppose  a  person  60  years  of  age  is  to  receive  an 
annual  salary  of  $600  during  life.  What  is  the  present  value 
of  such  income,  at  6  per  cent.;  compound  interest  ? 

Ans.  $4982.40. 

Ex.  3.  What  must  be  paid  for  a  life  annuity  of  $560  a 
year,  by  a  person  aged  55  years,  at  5  per  cent.,  compound  in- 
terest ?  Ans.  $5794.32. 

ART.  157.  To  find  how  large  a  life  annuity  can  be  bought 
for  a  given  sum,  by  a  person  of  a  given  age. 

Ex.  1.  How  large  a  life  annuity  can  be  purchased  for  $2400, 
by  a  person  aged  $65  years,  at  7  per  cent.  Ans.  $350.51. 

Operation. 

2400.000  ^  6.847  =  350.51. 

RULE. — Divide  the  given  sum  by  the  present  value  of  an 
annuity  of  $1  for  the  given  age  and  rate. 

Note. — This  is  the  reverse  of  the  preceding  article. 

Ex.  2.  How  large  a  pension,  at  6  per  cent.,  compound  in- 
terest, can  be  bought  for  $1600,  the  age  of  the  pensionary 
being  50  years  ? 

Ex.  3.  How  large  an  annuity  can  be  bought  for  $3000,  by 
a  person  aged  25  ;  interest,  5  per  cent.  ?  Ans.  190.15. 


ALLIGATION.  237 


ALLIGATION. 

ART.  158.  In  various  kinds  of  business,  it  is  sometimes 
convenient  or  necessary  to  mix  articles  of  different  values  or 
qualities,  thus  forming  a  compound  whose  value  or  quality 
differs  from  that  of  its  ingredients.  This  process  is  called 
ALLIGATION  (L.  ad,  to,  and  ligatus,  bound);  a  name  sug- 
gested by  the  method  of  solving  some  of  its  problems  by  join- 
ing or  binding  together  the  terms. 

The  various  problems  in  Alligation  may  be  divided  into 
two  classes,  commonly  called  Alligation  Medial  and  Alliga- 
tion Alternate. 


ALLIG-ATION    MEDIAL. 

ART.  169.  Alligation  Medial  teaches  the  method  of  find- 
ing the  average  value  or  quality  of  a  mixture,  the  value  or 
quality,  and  also  the  quantity,  of  whose  ingredients  are  known. 
Ex.  1.  A  farmer  mixed  together  50  bushels  of  oats,  at  40 
cents  per  bushel ;  30  bushels  of  barley,  at  50  cents  per  bushel ; 
and  25  bushels  of  corn,  at  60  cents  per  bushel.  What  was  a 
bushel  of  the  mixture  worth  ? 

Explanation. — Since  the  value  of  50 

OPERATION.  bushels  of  oats,  at  40  cents  a  bushel,  is 

cts.  CK  2000  cents  ;  of  30  bushels  of  barley,  at 

50  cents  a  bushel,  1500  cents  ;  and  25 
50x30=1500  ITT 

60x95=1500  bushels  of  corn,  at  60  cents  a  bushel, 

105  )5000  1500  cents  ;  the  value  of  the  mixture  is 

—477|  2000  cents+1500  cents  +  1500  cents= 

5000  cents.     But  the  mixture  contains 

50  bushels  +  30  bushels +25  bushels =105  bushels.  Hence,  the 
value  of  1  bushel  of  the  mixture  is  Tij  of  5000  cents=47i£ 
cents. 

Ex.  2.  A  goldsmith  melted  together  12  oz.  of  gold,  20 


238  ALLIGATION. 

carats  fine ;  6  oz.}  18  carats  fine  ;  and  10  oz.,  16  carats  fine. 
What  was  the  quality  of  the  mixture  ?  Ans.  18|  carats. 

Explanation. — Since  a  carat  of  gold 

OPERATION.  is  the  twenty-fourth  part  of  the  mass 

carats.  Carats.          regarded  as  a  unit   (here   an   oz.),   12 

7o  X     g  II  -IQO  oz.  of  gold,  each  oz.  containing  20  carats 

16  x  10  =  160  of  pure  gold,  contain  12  times  20  carats 

28     )508~         =240  carats  ;  6  oz.  of  gold,  each  con- 

~~18"i         taining  18  carats,  contain  108  carats  ; 

10  oz.  of  gold,  each  containing  16  carats, 

contain  160  carats.  Hence,  12  oz. +  6  oz.-f-lO  oz.=28  oz.  of 
mixture  contain  240  carats  +  108  carats  + 160  carats  =508 
carats,  and  1  oz.  of  the  mixture  must,  therefore,  contain  •£-§  of 
508  carats=18|  carats. 

Note. — The  regarding  of  a  carat  as  a  unit  of  measure  of  the 
pure  gold  in  a  given  mass  is  not  essential  to  the  explanation 
of  the  above  solution.  For,  suppose  the  comparative  qualities 
of  the  above  varieties  of  gold,  represented  respectively  by  the 
numbers  20,  18,  and  16.  Now,  as  these  numbers  represent 
the  comparative  qualities  of  the  three  varieties  of  gold,  it  is 
clear  they  must  contain  a  common  unit  of  quality.  The  num- 
ber 20  denotes  that  the  quality  of  the  first  variety  contains 
this  common  union  of  quality  20  times  ;  and,  hence,  20  is  the 
measure  of  its  quality.  But  the  effect  of  12  oz.  in  determining 
the  quality  of  a  mixture  is  12  times  as  great  as  the  effect  of 
1  oz.  ;  hence,  12  x  20  or  240,  is  the  effective  quality  of  12  oz. 
of  gold,  if  the  quality  of  1  oz.  is  20. 

RTJ3L.E. 

Multiply  the  value  or  quality  of  each  article  by  the  number 
of  articles ,  and  divide  the  sum  of  the  products  by  the  sum  of 
the  articles.  TJie  quotient  will  be  the  average  value  or  quality 
of  the  mixture. 

Ex.  3.  A  grocer  mixed  15  Ibs.  of  coffee,  at  18  cents  a 
pound  ;  35  Ibs.,  at  16  cents  a  pound  ;  and  40  Ibs.,  at  14  cents  a 
pound.  What  is  a  pound  of  the  mixture  worth  ?  Ans.  15£  cents. 

,Ex.  4.  A  grocer  mixed  25  gallons  of  wine,  at  90  cents  a 


ALLIGATION.  239 

gallon ;  40  gallons  of  brandy,  at  75  cents  a  gallon ;  and  10 
gallons  of  water  without  price.  "What  is  a  gallon  of  the  mix- 
ture worth  ?  Ans.  70  cents. 


ALLIGATION    ALTERNATE. 

ART.  160.  Alligation  Alternate  teaches  the  method  of 
finding  in  what  proportion  several  simple  ingredients,  whose 
values  or  qualities  are  known,  must  be  taken  to  form  a  mix- 
ture of  a  given  mean  value  or  quality. 

Sometimes  the  quantity  of  one  or  more  of  the  ingredients 
is  given,  and  it  is  required  to  find  what  amount  of  the  other 
ingredients  must  be  taken. 

Sometimes  the  quantity  of  the  mixture  is  given,  and  the 
relative  amount  of  ingredients  is  required. 

We  shall  give  the  solution  of  examples  involving  the  last 
two  conditions,  but  omit  special  rules. 

Ex.  1.  A  grocer  has  coffees  worth  10  and  15  cents  a  pound. 
In  what  proportion  must  they  be  taken  that  the  mixture  may 
be  sold  for  13  cents  a  pound  ? 

Solution. — By  selling  the  mixture  for  13  cents  a  pound,  he 
will  gain  3  cents  on  each  pound  of  the  coffee  worth  10  cents, 
and  will  lose  2  cents  on  each  pound  of  the  coffee  worth  15 
cents.  Hence,  to  counterbalance  the  gain  of  3  cents  on  1 
pound  of  the  first  kind,  he  must  use  l£  (3n-2)  pounds  of  the 
second  kind.  The  proportion,  therefore,  must  be  1  lb.,  worth 
10  cents,  to  li  Ibs.,  worth  15  cents. 

Ex.  2.  A  grocer  has  sugars  worth  7,  10,  and  12  cents  a 
pound.  In  what  proportion  must  they  be  taken  to  make  a 
mixture  worth  9  cents  a  pound  ? 

Solution. — On  each  pound  of  sugar  worth  7  cents  there  is 
a  gain  of  2  cents,  and  on  each  pound  of  sugar  worth  10  cents 
there  is  a  loss  of  1  cent.  He  must,  therefore,  take  2  pounds  of 
the  second  that  the  loss  may  counterbalance  the  gain  on  1  pound 
of  the  first.  On  each  pound  of  sugar  worth  12  cents  there  is 
a  loss  of  3  cents.  To  counterbalance  this  loss  1|  (3-=-2)  pounds 


940  ALLIGATION. 

more  of  the  first  kind  must  be  taken.  Hence,  the  proportion 
is  1  +  1^—21  Ibs.  worth  7  cents,  to  2  Ibs.  worth  10  cents,  to  1 
Ib.  worth  12  cents. 

Ex.  3.  A  grocer  has  four  kinds  of  tea,  worth  respectively 
50,  60,  70,  and  90  cents  a  pound.  In  what  proportion  must 
they  be  taken  to  make  a  mixture  worth  80  cents  a  pound  ? 

Solution. — On  a  pound  of  the  first  kind  there  is  a  gain  of 
30  cents  ;  on  a  pound  of  the  second,  a  gain  of  20  cents  ;  on  a 
pound  of  the  third,  a  gain  of  10  cents  ;  and,  hence,  on  a  pound 
of  each  of  these  three  kinds  a  gain  of  30+20+10—60  cents. 
On  1  pound  of  the  fourth  kind  there  is  a  loss  of  10  cents  ;  and, 
hence,  to  counterbalance  the  60  cents  gain,  6  pounds  of  the 
fourth  kind  must  be  taken.  The  proportion  is,  therefore,  1 
Ib.  of  the  first  kind,  to  1  Ib.  of  the  second,  to  1  Ib.  of  the  third, 
to  6  pounds  of  the  fourth  or  multiples  of  these  numbers. 

Ex.  4.  A  farmer  has  oats  worth  40  cents  a  bushel ;  corn, 
worth  50  cents  ;  rye,  worth  70  cents  ;  and  wheat,  worth  .90 
cents.  How  must  they  be  mixed  that  the  mixture  may  be 
worth  60  cents  ? 

Solution. — On  each  bushel  of  oats  there  is  a  gain  of  20 
cents  ;  on  each  bushel  of  wheat  a  loss, of  30  cents.  Hence,  he 
must  take  \\  bushel  of  oats  to  1  bushel  of  wheat.  On  each 
bushel  of  corn  there  is  a  gain  of  10  cents  ;  on  each  bushel  of 
rye,  a  loss  of  10  cents.  Hence,  he  must  take  1  bushel  of  corn 
to  1  of  rye.  Proportion,  li,  1,  1,  1. 

Note. — In  the  above  solutions,  it  will  be  observed  that  the 
ingredients  are  combined,  two  and  two,  in  such  quantities  as 
to  make  gains  and  losses  EQUAL. 

METHOD      BY.    LINKING. 

3d  Example  above. 


80 


50x          -        -     10 
60  \\         -        -     10 

70  0;     -     -   10 


Ans.,  or  Ans.  Verifications. 


4-10= 


90'  30  +  20  +  10=60 


10x50=  500  1x50=  50 

10x60=  600  1x60=  60 

10x70=  700  1x70=  70 

60x90=5400  6x90=540 


90  )7200     9          )720 

~80"  ~80~ 


'40 
50 


ALLIGATION.  241 

4th  Example. 

Ans.,  or  Ans.  Verifications. 

3     30x40=1200  3x40=120 

1      10x50=  500  1x50=  50 

1  10x70=  700  1x70=  70 

2  120x90=1800  2x90=180 
70          )420Q  7           )420 

60  60 

Or  thus  : 

or  Ans.  Verifications. 

10x40=  400  1x40=  40 

30  x  50= 1500  3  x  50=  150 


607(X)     -    -    20f~1~10      |2     J20x70=1400  2x70=140 

|10  x  90=  900  1x90=  90 

70           )4200  7           )42Q 

60  60 

RULE. 

Write  the  values  or  qualities  of  the  ingredients  in  a  column, 
and  the  value  or  quality  of  the  mixture  at  the  left  hand.  Link 
each  number  in  the  column  that  is  LESS  than  the  value  or  qual- 
ity of  the  mixture  icith  one  that  is  GREATER,  or  the  reverse. 

Then  find  the  difference  between  the  value  or  quality  of  the 
mixture  and  that  of  each  ingredient,  and  place  the  same  oppo- 
site the  number  with  which  it  is  connected.  The  number,  or 
the  sum  of  the  numbers,  opposite  the  value,  or  quality  of  each 
ingredient,  ivill  denote  the  amount  of  the  same  to  be  taken. 

Remark. — Since  equi-multiples  of  quantities  have  the  same 
relation  to  each  other  as  the  quantities  themselves,  it  follows 
that  any  equi-multiples  of  these  numbers  will  also  satisfy  the 
conditions  of  the  problem. 

Ex.  5.  A  merchant  has  teas  worth  60,  75,  80,  and  100  cents 
per  Ib.  How  much  of  each  kind  must  he  take  to  make  a  mix- 
ture worth  85  cents  per  Ib.  ?  "  Ans.  1,  1,  1,  2. 

Ex.  6.  A  wine-merchant  wishes  to  mix  wine  worth  $1.20 
and  $1.40  per  gallon,  with  water.  How  much  of  each  kind 
must  he  use  to  make  a  mixture  worth  $1.00  per  gallon  ? 

Ex.  7.  A  goldsmith  wishes  to  combine  gold  22  carats  fine  ; 

19  carats  fine  ;  18  carats  fine ;  and  17  carats  fine.     In  what 

16 


242 


ALLIGATION. 


proportion  must  they  be  united  that  the  compound  may  be  20 
carats  fine  ? 

Ex.  8.  A  farmer  wishes  to  mix  60  bushels  of  corn,  at  60 
cents  a  bushel,  with  rye,  at  75  cents.;  barley,  at  50  cents  ;  and 
oats  at  45  cents.  What  quantity  of  rye,  barley,  and  oats 
must  be  taken  that  the  mixture  may  be  worth  65  cents  a 
bushel  ? 

Explanation. — Since 
the  amount  of  corn  to 
be  taken  is  6  times 
the  amount  found — 10 

[240 


65 


OPERATION. 
45N         -  10") 

50\\    -        -       10 

eoO;   -  10 

75' 20+15  +  5=40 


bushels — the  quantity 
of  oats,  barley,  and 
rye,  must  be  increased  in  the  same  ration :  i.  e.,  be  multi- 
plied by  6. 

Ex.  8.  A  grocer  wishes  to  mix  100  pounds  of  coffee,  worth 
12  cents,  with  coffee  worth  15,  10,  and  8  cents.  What  quan- 
tities must  he  take  that  the  mixture  may  be  worth  11  cents  a 
pound  ? 

10.  A  wine-merchant  wishes  to  fill  a  cask  containing  36 
gallons  with  a  mixture  of  wines  worth  $1.00,  $1.20,  $1.50, 
and  $1.60  per  gallon.  How  many  gallons  of  each  kind  must 
he  take  that  the  mixture  may  be  worth  $1.40  per  gallon  ? 


Operation. 


Or  thus 


8 

201 

21 

4 

8 

10  1 

20  1 

•M0=|     > 

16 

40  I 

4J 

9 

36^9=4 

Ans. 

8 
4 
8 

I6 
36 


Explanation. — Since,  in  the  first  case,  the  amount  required 
— 36  gallons — is  f  of  the  amount  obtained  by  mixing  20  gal- 
lons of  the  first  kind,  10  gallons  of  the  second,  20  .gallons 
of  the  third,  and  40  of  the  fourth,  it  is  evident  that  f  of  the 
quantity  of  each  ingredient  must  be  taken.  In  the  second 
case,  the  amount  required  is  4  times  the  amount  obtained  ; 


PARTNERSHIP.  243 

and,  hence,  the  quantity  of  each  ingredient  must  be  multi- 
plied by  4. 

Ex.  11.  A  trader  wishes  to  fill  10  casks,  each  containing  28 
gallons,  with  a  mixture-  of  brandy,  rum,  and  water.  If  the 
brandy  is  worth  80  cents  a  gallon,  and  the  rum  95  cents,  how 
many  gallons  of  each  must  be  taken  that  the  mixture  may  be 
worth  75  cents  ? 


PARTNERSHIP. 

ART.  161.  Partnership  is  the  association  of  two  or  more 
persons,  for  the  purpose  of  carrying  on  business  at  their  joint 
expense. 

Each  person  thus  associated  is  called  a  partner  ;  and  the 
several  partners,  in  their  associated  capacity,  are  called  a  com- 
pany, firm,  or  house. 

The  money  or  property  invested  by  such  a  company  in 
business  is  called  their  capital,  or  joint-stock,  or  stock  in  trade. 

The  profits  and  losses  of  the  business  are  sometimes  shared 
by  the  several  partners  in  proportion  to  their  stock  in  trade  ;  or 
more  correctly,  in  proportion  to  the  use  or  interest  of  their  stock 
in  trade.  When  the  stock  of  the  several  partners  is  invested  for 
the  same  length  of  time  the  interest  of  the  stock  is  proportioned 
to  the  stock  itself]  and,  hence,  the  profits  and  losses  in  this 
case  are  shared  in  proportion  to  the  stock  of  the  several  partners. 

Sometimes  one  or  more  of  the  partners  furnish  the  capital, 
and  the  other  or  others  contribute  their  services. 

The  profit  or  loss  to  be  shared  is  called  a  dividend. 

The  duration  of  a  partnership  is  limited  by  contract,  or  is 
left  indefinite,  subject  to  be  dissolved  by  mutual  consent  and 
agreement. 

When  a  company  is  dissolved,  either  by  the  limitations  of 
the  contract  or  by  mutual  agreement,  the  adjustment  of  the 
accounts  of  the  company,  and  the  division  of  effects,  is  called 
a  partnership  settlement. 


244  PARTNERSHIP. 

Note. — Although  partnership  settlements  fall  properly 
within  the  province  of  book-keeping,  we  have  added  a  few  ex- 
amples to  illustrate  the  manner  of  closing  such  accounts. 

ART  162.  When  the  capital  of  the  several  partners  is 
invested  for  the  same  length  of  time,  to  find  each  partner's 
share  of  the  profit  or  loss. 

Ex.  1.   A,  B,  and  C  enter  into  partnership  in  the  lumber 
business  for  3  years.     A  put  in  $2400 ;  B,  3600;  C,  $600.€> 
At  the  time  of  the  dissolution  of  the  firm  the  net  profits  were 
$4000.     What  is  each  partner's  share  of  the  profits  ? 

FIRST     METHOD. 

A's  stock,  $2400=TVo0o°o  =  }  of  entire  stock. 

B's    "         3600=TY¥Yo  =  r3o     " 

C's     "         6000=^7^=  \     "        " 

Entire  stock,  $12000 

Hence,  A's  share  of  profits=  }  of  $4000— $  800 
B's  "  "  =  y\rof  $4000=  1200 
C's  "  =1  of  $4000=  2000 

Entire  profits,          ....         $4000 

Explanation. — Since  A's  stock  equals  },  B's  r3o ,  and  G's  j 
of  the  entire  stock,  A  would  be  entitled  to  },  B  to  T\,  and  C 
to  J  of  the  entire  profits. 

SECOND     METHOD. 

A's  stock,  $2400 

B's     "        3600 

C's      "        6000 

Entire  stock,     $12000 

"     profits,    $4000 

TVoVo  =  f     Hence,  profits=  %  of  stock. 

A's  share  of  profits^  of  $2400=$  800 

B's     "        "          =1  of  $3600=  1200 

C's      "        "          =iof$6000=_2000 

Entire  profits,         ....      $4000 

Explanation. — Since  the  entire  profits  equal  i  of  the  entire 
stock,  each  partner's  share  of  the  profits  must  equal  i  of  his 
stock. 


PARTNERSHIP.  245 

THIRD     METHOD. 

$4000-^$12000=.33i.  Hence  the  profits=33j-  per  cent, 
of  the  stock. 

A's  share  of  profits =$2400  x. 33  i=$  800 

B's     "        "          =  3600  x. 33i=   1200 

C's      "        "          =  6000x.33j=  2000 

Entire  profits,  .  .  $4000 

FOURTH     METHOD. 

S 12000  :  §2400  :  :  §4000  :  8  800,  A's  profits. 
§12000  :  $3600  :  :  $4000  :  $1200,  B's      " 
§12000  :  $6000  :  :  §4000  :  $2000,  C's      " 

$4000,  Entire  profits. 

EULE. — First  find  WHAT  PART  of  the  entire  stock  each 
partner  has  contributed,  then  take  the  SAME  PART  of  the  total 
profits  or  loss  for  each  partner's  share  of  the'  same. 
Or, 

First  find  WHAT  PART  of  the  entire  stock  the  total  profits 
or  loss  may  be  ;  then  take  the  SAME  PART  of  each  partner's 
stock  for  his  share  of  the  profits  or  loss. 
Or, 

Find  what  per  cent,  of  the  entire  stock  the  total  profits  or 
loss  may  be  ;  then  multiply  each  partner's  stock  by  the  rate 
per  cent,  expressed  decimally. 
Or, 

Form  the  proportion ,  as  the  ivhole  stock  is  to  each  partner' s 
stock,  so  is  the  whole  profit  or  loss  to  each  partner's  profit  or 
loss. 

Ex.  2.  A,  B,  and  C  traded  in  company.  A  put  in  $8000  ; 
B,  $4500  ;  and  C,  $3500.  Their  profits  were  $6400.  What  is 
each  partner's  share  of  the  profits  ?  Ans.  C's  $1400. 

Ex.  3.  A  and  B,  in  trading  for  three  years,  make  a  profit 
of  $4800.  A  invested  f  as  much  stock  as  B.  What  is  each 
man's  share  of  profit  ?  Ans.  B's  $3000. 

Ex.  4.  Two  drovers,  A  and  B,  have  been  operating  in  com- 
pany in  buying  and  selling  sheep.  A  made  purchases  to  the 
amount  of  $6780,  and  paid  expenses  amounting  to  $274.12. 
B  made  purchases  to  the  amount  of  $3840,  and  paid  expenses 


246  PARTNERSHIP. 

amounting  to  $312.  The  sheep  were  sold  by  A  for  $10,482. 
How  much  was  made  or  lost  ?  How  will  A  and  B  settle,  the 
profits  or  losses  to  be  shared  equally  ? 

Ex.  5.  C  and  D  agree  to  perform  a  certain  piece  of  work 
for  government,  for  which  they  are  to  receive  $4680,  provided 
it  passes  inspection  as  No.  1.  If  it  pass  as  No.  2,  15  per  cent. 
is  to  be  deducted  ;  as  No.  3,  20  per  cent,  is  to  be  deducted. 

The  result  of  the  inspection  was  as  follows  : 

1st  division,  which  is  £  of  contract,  is  No.  1. 
2d         "  "       i  "  No.  3. 

2d         "  "       J  "  No.  2. 

C  has  advanced,  for  the  prosecution  of  the  work,  $1328  ; 
B  has  advanced  $987.45.  Neither  has  received  anything  from 
government,  and  all  the  money  advanced  has  been  used.  How 
much  have  they  gained,  and  what  is  each  man's  share  ? 

ART.  163.  When  the  capital  is  invested  for  different  periods 
of  time,  to  find  each  partner's  share  of  the  profits  or  loss. 

Ex.  1.  A,  B,  and  C  traded  in  company.  When  they  com- 
menced business,  A  put  in  $4000  ;  B,  $3000  ;  and  C,  $5000. 
At  the  close  of  the  first  year  A  put  in  $3000  more,  and  C  took 
out  $1000.  At  the  close  of  the  second  year  B  put  in  $2000. 
At  the  close  of  the  third  year  they  dissolve  partnership,  and 
the  net  profits  of  the  firm  are  found  to  be  $2100.  What  is 
each  partner's  share  of  the  gain  ? 

Operation. 
fc  SS    «4000+«14000=?18000. 


A,  B,  and  C,  together,  had  in  $42000  for  one  year. 

Hence,  A's  share  of  gam=}f  Hf  or  •?  of  $2100=$900 
"      B's  "          ={i7fUor  11  of  $2100=$550 

"      C's  "         =i|$n  or  i|  of  $2100=$650 

Entire  profits,          .  .        .        $2100 


PA-RTNERSHIP.  247 

Explanation.—  Since  A  had  in  $4000  for  1  year,  and  $7000 
for  2  years  =$14000  for  1  year,  A  had  in  trade  the  same  as 
$4000  +  $14000=§1SOOO  for  1  year  ;  and,  since  B  had  in  $3000 
for  2  years=6000  for  1  year,  and  $5000  for  1  year,  B  had  in 
trade  the  same  as  $6000  +  $5000=  $11000  for  1  year;  and 
since  C  had  in  $5000  for  1  year,  and  §4000  for  2  years  =$8000 
for  1  year,  C  had  in  trade  the  same  as  $5000  +$8000=  $13000 
for  1  year.  '  Hence,  A,  B,  and  C,  together,  had  in  trade  the 
same  as  $18000  +$1100  +$13000=  $42000  for  1  year. 

Note.  —  The  remaining  portion  of  the  solution  may  be  in 
accordance  with  either  of  the  four  preceding  rules  ;  for  the 
time  the  stock  of  the  several  partners  is  invested  is  now  the 
same—  one  year—  A's  stock  being  $18000  ;  B's,  $11000  ;  and 
C's,  $13000. 

BY     INTEREST. 

Years.  Int.  Int. 

A  had  in  $4000  for  1=  §240.00  )  _ 
$7000  for  2=$840.00  \  - 
B    "        §3000  for  2=$360.00  )  _ 
"        $5000  for  1=  $300.00  \  ~ 
C     "        §5000  for  1  =  $300.00  )  _ft  f-ftftm 

§4000  for  2=  $480.00  S~ 
Total  interest  of  entire  stock,  at  6^=  $2520.00 

Hence,  A's  share  of  profits=  4^4  §  or  f   of  $2100=900 
B's  "  =AVTor  U  of  $2100=550 

C's  "  =/5Vff  or  if  of  $2100=650 


" 


Note.  —  Since  like  parts  of  two  numbers  have  the  same  ratio 
as  the  numbers  themselves,  it  is  evident  the  interest  may  be 
computed  at  any  per  cent.  It  is  also  evident,  from  the  same 
principle,  that  the  interest  of  the  stock  may  be  regarded  as  the 
stock  itself;  and,  hence,  when  the  interest  is  obtained,  the 
remaining  portion  of  the  solution  may  be  in  accordance  with 
either  of  the  four  preceding  rules. 

RULE.  —  Multiply  each  partner's  stock  by  the  time  it  was 
invested,  and  regard  the  product  as  his  stock  in  trade,  and  the 
SUM  of  the  products  as  the  entire  stock  in  trade,  and  then  pro- 
ceed according  to  either  of  the  four  preceding  rules. 


248  PARTNERSHIP. 

Or, 

Find  the  interest  of  each  partner's  stock  for  the  time  it  ivas 
invested,  and  regard  the  interest  thus  found  as  his  stock  in 
trade,  and  the  SUM  of  the  interests  as  the  entire  stock  in  trade, 
and  then  proceed '  in  accordance  with  either  of  the  four  pre- 
ceding rules. 

Ex.  2.  A  and  B  entered  into  partnership  Jan.  1,  1858.  A 
put  in  $4500,  and  B,  $5500.  July  1,  1858,  B  put  in  $1500 
more.  Oct.  1, 1858,  A  took  out  $500.  Jan.  1,  1859,  each  put 
in  $1500.  July  1, 1859,  they  dissolved  partnership,  and  found 
they  had  lost  $846.  What  is  each  partner's  share  of  the 
loss  ?  Ans.  A's  $342. 

B's  $504. 

Ex.  3.  A,  B,  and  C  hired  a  pasture  for  6  months,  for  $245. 
A  put  in  40  sheep  ;  B,  50  sheep  ;  C,  80  sheep.  At  the  close 
of  3  months  A  put  in  20  more  ;  at  the  close  of  4  months  B 
took  out  20 ;  and  at  the  close  of  5  months  C  took  out  60. 
How  much  ought  each  to  pay  ?  Ans.  A  $75. 

B    $65. 
C  $105. 

Ex.  4.  A  and  B  enter  into  a  partnership  for  3  years.  A 
put  in  $10000,  and  B,  $2500.  B  is  to  do  the  business,  and 
his  services  are  to  be  regarded  as  worth  the  use  of  $7500,  the 
difference  between  his  and  A's  stock.  At  the  close  of  the  first 
year  A  increased  his  stock  to  $18000.  At  the  close  of  the  3 
years  the  partnership  closed,  and  a  net  gain  found  of  $9500. 
What  is  each  partner's  share  of  the  gain  ?  Ans.  A's  $5750. 

Bs  $3750. 


DUODECIMALS.  249 


DUODECIMALS. 

ART.  164.  A  Duodecimal  (Latin  duodecim,  twelve)  is  a 
number  whose  scale  is  12  ;  hence,  12  units  of  any  order  make 
one  unit  of  the  next  higher  order. 

This  system  of  numbers  is  used  by  artificers  in  finding  the 
contents  of  surfaces  and  solids.  For  this  purpose  the  foot  is 
divided  into  12  equal  parts  called  inches  or  primes,  marked  ' ; 
the  inch  or  prime  is  divided  into  12  equal  parts  called  seconds, 
marked  ",  &c.  The  accents  used  to  mark  the  different  orders 
are  called  indices. 

TABLE. 

12  fourths  ("")    make  1  third  ('") 

12  thirds  "  1  second  (") 

12  seconds  "  1  inch  or  prime  (') 

12  inches  or  primes  "  1  foot  (ft.) 

Note. — Duodecimals  may  be  added  and  subtracted  like 
Denominate  Numbers. 


MULTIPLICATION    OF    DUODECIMALS. 

ART.  165.    To  multiply  one  duodecimal  by  another. 
Ex.  1.  How  many  square  feet  in  a  board  9  ft.  5  in.  long; 
and  2  ft.  8  in.  wide  ? 

Operation. 

9  ft.      5'  Explanation. — Since  8'=  r\  of  a  foot, 

2  ft.      8^  and  5'=T5T,  8'  x5'=  -fs  x  T^=TyT=40'= 

;'  4"        3,  g,      ^yrjte  4*  jn  secon(is  order.     Again, 

18         10'  since  8'=  fc,  9  ft,  x  8'=9  ft.  x  I«7=f|=72/ 

25 sq.ft.  1  and  72'+ 3'   (above)  =  75'=  6  sq.  ft.   3'. 

Hence  9  ft.  5'  x  8;=6  sq.  ft.  3'  4".     Again  5'  or  T\  x  2  ft.=  | } 

=10'  and  9  ft.x2  ft.=18  sq.  ft.     Hence  9  ft.  5'x2  ft.  =  18 


250         MULTIPLICATION      OF     DUODECIMALS. 

sq.  ft.  10'.1  Adding  these  two  products,  the  total  product  is 
25  sq.  ft.  I'  4". 

It  will  be  observed  that  the  denomination  of  the  product 
of  any  two  denominations  is  denoted  by  the  sum  of  their  inj 
dices;  thus  5'  xS"=40'",  6"x4"=24"",  &c. 

In  the  above  process,  the  notations  of  feet,  primes,  &c.,  are 
used  for  convenience.  The  multiplier  is,  however,  really  an 
abstract  number. 

R.TJH.E. 

Write  the  Multiplicand  under  the  Multiplier,  placing  ft. 
under  ft.,  primes  under  primes,  &c. 

Beginning  at  the  lowest  order,  multiply  each  order  of  the 
multiplicand  by  each  order  of  the  multiplier,  adding  their  in- 
dices to  ascertain  the  denomination  of  the  product,  and  carrying 
one  for  every  twelve  from  a  lower  order  to  the  next  higher. 

Add  the  several  partial  products  for  the  product  required. 

!E  x  a  m.  pies. 

2.  Multiply  12  ft.  8'  by  4  ft.  10'.     Ans.  61  sq.  ft.  2'  8". 

3.  Multiply  4  ft.  6'  4"  by  8  ft.  8'.    Ans.  39  sq.  ft.  2'  10"  8'". 

4.  Multiply  10  ft.  6'  6"  by  4'  8". 

5.  How  many  square  feet  in  a  board  12  ft.  9  in.  long  and 
11'  4"  wide  ?  Ans.  12  sq.  ft.  2'  6". 

6.  How  many  cubic  inches  in  a  block  2  ft.  9'  long,   1  ft.  8' 
wide,  and  2  ft.  4'  high  ? 

7.  Kequired  the  solid  contents  of  a  block  4  ft.  4'  long,  2  ft. 
3'  wide,  and  10'  high. 

8.  How  many  square  feet  in  GO  boards,  each  board  being 
15  ft.  4'  long,  and  1  ft.  2'  wide  ? 

9.  Divide  10  sq.  ft.  2'  10"  by  5  ft.  7'.       .  Ans.  1  ft.  10'. 

Remark. — By  observing  that  division  is  the  reverse  of  mul- 
tiplication, the  following  process  will  be  readily  understood. 
The  divisor  is  placed  at  the  right  of  the  dividend  for  con- 
venience. 


INVOLUTION.  251 

DIVIDEND.  DIVISOR. 

lOsq.  ft.  2'  10"  I  5ft.    r 

j> T  1  fr.  10',  Quotient. 

4—     —?>  10" 
4_        r  10" 

10.  Divide  62  sq.  ft.  11"  3'"  by  8  ft.  6'  9".     Am.  7  ft.  3'. 


INVOLUTION. 

ART.  166.  Involution  is  the  method  of  finding  the  powers 
of  numbers  or  quantities. 

The  power  of  a  number  (except  the^rsO  is  the  product  ob- 
tained by  multiplying  the  number  by  itself  one  or  more  times. 

The  first  power  of  a  number  is  the  number  itself.  It  is 
also  called  the  root. 

The  second  power,  or  square,  is  the  product  of  the  number 
multiplied  by  itself  once. 

The  third  power,  or  cube,  is  the  product  of  the  number 
multiplied  by  itself  twice. 

The  different  powers  derive  their  .names  from  the  number 
of  times  the  number  is  taken  as  a  factor.  Thus,  the  first 
power  contains  the  number  as  a  factor  once  ;  the  second 
power,  twice;  the  third  power,  three  times,  &c. 

The  index  or  exponent  of  a  power  is  a  small  figure  placed 
at  the  right  and  a  little  above  the  number,  to  show  the  degree 
of  the  power,  or  how  many  times  the  number  is  taken  as  a 
factor. 

The  0  power  of  any  number  or  quantity  results  from  di- 
viding the  number  by  itself  and  is  equal  to  unity  or  1.  Thus, 
6°=1,  25°=1,  50°= 1,  &c. 

The  following  table  will  illustrate  the  above  definitions 
and  remarks. 

5°(5-7-5)=l,  the  0  power  of  5. 

51— 5,  the  first  power  or  root  of  5. 

5- =5  x  5=25,  the  second  power  or  square  of  5. 


252  INVOLUTION. 

53=5  x  5  x  5=125,  the  third  power  or  cube  of  5. 
54=5x5x5x 5=625,  the  fourth  power  of  5. 
55=5  x  5  x  5  x  5  x  5=3125,  the  fifth  power  of  5. 
Remark. — The  second  power  of  a  number  is  called  its 
square ,  because  the  area  of  a  geometrical  square  is  obtained 
by  multiplying  the  number  of  linear  units  in  one  of  its  sides 
by  itself  once.     The  third  power  is  called  the  cube,  because 
the  solid  contents  of  a  geometrical  cube  is  obtained  by  multi- 
plying the  number  of  linear  units  in  one  of  its  sides  by  itself 
twice. 

Ex.  1.  What  is  the  cube  or  third  power  of  24  ? 

Operation. 
24,  1st  power. 
24 

96  It  is  evident  from  the  definition  that 

the  cube  of  a  number  is  obtained  by  inul- 

576,  2d  power.      tiplying  the  number  by  itself  twice,  or  by 

taking  it  three  times  as  a  factor. 
2304 
1152 
13824,  3d  power. 

RULE. — Multiply  the  number  by  itself  as  many  times  as 
there  are  units  in  the  exponent  of  the  power,  LESS  ONE.  The 
last  product  will  be  the  required  power. 

NOTE. — The  power  of  a  fraction,  either  common  or  decimal, 
is  found  in  the  same  manner. 

Examples. 

2.  What  is  the  square  of  204  ?  Ans.  41616. 

3.  What  is  the  4th  power  of  25  ? 

4.  What  is  the  cube  of  ±  ?  Ans.  7Vj. 

5.  What  is  the  square  of  2.5  ? 

6.  What  is  the  4th  power  of  .04  ?  Ans.  .00000256. 

7.  What  is  the  5th  power  of  1  ? 

8.  What  is  the  9th  power  of  12  ? 

SUGGESTION. — Since  the  product  of  two  or  more  powers  of 
a  given  number  is  the  power  denoted  by  the  sum  of  their  ex- 


EVOLUTION.  253 

ponents,  the  9th  power  of  12  may  be  found  by  multiplying  the 
the  3d  power  by  itself  twice  ;  thus,  123  x  123  x  123=129. 
9.  What  is  the  4th  power  of  2j  ?  Ans.  39T'? 

10.  What  is  the  3d  power  of  2.04  ? 

11.  What  is  the  value  of  154  ? 

12.  What  is  the  value  of  (f )'  ?  Ans.  ^\. 

13.  What  is  the  value  of  201s  ? 

14.  What  is  the  value  of  .OOP  ? 

15.  What  is  the  square  of  9 J  ?  Ans.  85TV 


EVOLUTION. 

ART.  167.  Evolution  is  the  method  of  finding  the  roots 
of  numbers  or  quantities. 

Evolution  is  the  reverse  of  involution.  In  the  latter,  the 
root  is  given  to  find  the  power.  In  the  former,  the  power  is 
given  to  find  the  root. 

The  root  of  a  number  is  such  a  number  as  multiplied  by 
itself  a  certain  number  of  times,  will  produce  the  given 
number. 

The  first  root  of  a  number  is  the  number  itself.  It  is  also 
called  the  first  power. 

The  second,  or  square  root  of  a  number  is  that  number 
which,  multiplied  by  itself  once,  "411  produce  the  given 
number. 

The  third,  or  cube  root  must  be  multiplied  by  itself  twice 
to  produce  the  given  number. 

The  different  roots  take  their  names  from  the  number  of 
times  they  are  taken  as  factors  to  produce  the  given  number. 
The  first  root  is  taken  once  as  a  factor  ;  the  second  or  square 
root,  twice;  the  third  or  cube  root,  three  times,  &c. 

A  root  of  a  number  may  be  defined  to  be  a  factor 
which  taken  a  certain  number  of  times,  will  produce  the  given 
number. 

The  root  of  a  number  is  usually  indicated  by  the  radical 
sign  4/  placed  before  it,  with  the  index  of  the  root  written 
above  it. 


254  SQUARE     BOOT. 

Thus,  1/64  shows  that  the  3d  root  of  64  is  to  be  taken  ;  V§T, 
the  4th  root  of  81  ;  V15,  the  1st  root  of  15,  &c. 

The  index  is  usually  omitted  in  case  of  the  second  or 
square  root.  Thus,  v/64  or  V64  equally  indicates  the  square 
root  of  64. 

The  root  of  a  number  may  also  be  indicated  by  a  fractional 
exponent,  placed  on  the  right  of  the  number.  Thus  16*  indi- 
cates the  square  root  of  16  ;  81^,  the  fourth  root  of  81. 

12^  denotes  that  the  cube  root  of  the  square  of  12  is  to 
be  taken. 

A  number  may  be  either  the  perfect  or  imperfect  power  of 
a  required  root.  25  is  a  perfect  square,  but  an  imperfect  cube. 
The  exact  root  of  an  imperfect  power  can  not  be  extracted  and 
is  called  a  surd.  Prime  numbers  are  imperfect  powers  of  all 
their  roots,  except  the  first. 


SQUARE    ROOT. 

ART.  168.  The  Square  Root  of  a  number  is  a  number 
which  multiplied  by  itself  will  produce  the  given  number. 
Thus  the  square  root  of  16  is  4,  since  4  x  4=16. 

The  process  of  finding  the  square  root  of  a  number  is  best 
understood  by  observing  the  manner  in  which  the  square  of 
a  number  is  formed,  and  the  relation  which  the  orders  of  the 
square  bear  to  those  of  the  root. 

The  first  nine  numbers  are  : 

.  1,      2,      3,      4,      5,      6,      7,      8,      9, 
and  their  squares 

1,      4,   .  9,     16,    25,    36,    49,    64,    81. 
From  which  it  is  seen  that  the  square  of  any  number  composed 
of  one  order  of  figures,  can  not  contain  more  than  two  orders. 

Conversely,  that  the  square  root  of  any  number  composed 
of  one  or  two  orders  is  composed  of  but  one  order. 

It  will  further  be  seen  that  the  numbers  in  the  second  line 
above  are  the  only  perfect  squares  found  below  100,  and  that 


SQUARE      BOOT.  255 

the  square  root  of  any  number  between  any  two  of  these  con- 
secutive perfect  squares  is  between  the  two  corresponding  roots 
above.  Thus,  75  is  not  a  perfect  square  and  its  square  root 
is  between  8  and  9. 

The  first  nine  numbers  expressed  by  tens  are, 
10,      20,      30,       40,        50,        60,        70,        80,        90, 
and  their  squares, 

100,  400,  900,  1600,  2500,  3600,  4900,  6400,  8100. 
From  which  it  is  seen  that  the  square  of  tens  gives  no  order 
below  hundreds  or  above  thousands.  In  the  same  manner  it 
may  be  shown  that  the  square  of  any  number  must  contain  at 
least  twice  as  many  orders,  less  one,  as  the  number  squared. 
If  the  left  hand  figure  of  the  number  squared  is  more  than 
three,  the  square  will  always  contain  just  twice  as  many  or- 
ders as  the  root.  Thus,  the  square  of  456  contains  six  orders. 

Again,  every  number  may  be  regarded  as  composed  of  tens 
and  units.  Thus,  65  is  composed  6  tens  and  5  units,  that  is 
60+5=65  ;  365,  of  36  tens  and  5  units,  that  is  365=360+5. 
Hence(65)2=(60)'+2  x  60  x  5 +  (5) '=3600 +600 +25 =4225, 
and  (365)*=  (360)2  +  2  x  360x5+ (5) 2=  129600+3600+25= 
133225. 

In  like  manner  it  may  be  shown  that  the  square  of  any 
number  is  equal  to  the  square  of  the  tens  plus  twice  the  product 
of  tens  by  units  plus  the  square  of  units. 

The  two  principles,  above,  determine  the  process  of  extract- 
ing the  square  root  of  a  number. 

Ex.  1.  What  is  the  square  root  of  4225  ? 

Operation.  Explanation. — Since  4225  is  composed 

4225;65    of  four  orders,  its  root  will  be  composed 

of  but  two  ;  and  since  the  square  of  units 

6x2=12  5)625        is  composed  of  units  and  tens,  and"  the 

/^O    •-•  XT 

square  of  tens,  of  hundreds  and  thousands, 
we  separate  the  number  into  periods  of  two  figures  each,  by 
placing  a  dot  over  units  and  another  over  hundreds. 

Xow  42  must  contain  the  square  of  the  ten's  figure  of  the 
root.  The  greatest  perfect  square  in  42  is  36,  the  square  root 
of  which  is  6.  Hence  6  is  the  ten's  figure  of  the  root.  Sub- 


256  SQUARE     BOOT. 

trading  the  square  of  the  ten's  figure  of  the  root  from  42  hun- 
dreds, we  have  6  hundreds  for  a  remainder,  to  which,  if  the 
25  units  be  added,  we  shall  have  625,  which  is  composed  of 
twice  the  product  of  the  tens  of  the  root  by  the  units  (to  be 
found)  plus  the  square  of  the  units. 

Now  the  product  of  tens  by  units  gives  no  order  below 
tens,  hence  62  tens  must  contain  twice  the  product  of  the  tens 
by  the  units.  It  may  contain  more,  since  the  square  of  units 
may  give  tens. 

If  62  tens  be  divided  by  2  x  6  tens,  or  12  tens,  the  quotient, 
5,  will  be  the  unit  figure  of  the  root.  By  placing  5,  the  unit 
figure,  at  the  right  of  12  tens,  and  multiplying  the  result,  125, 
by  5,  the  product  will  be  twice  the  tens  by  the  units,  plus  the 
square  of  the  units. 

Ex.  2.  What  is  the  square  root  of  133225  ? 

133225(365,  Ans. 
3x3=        9 
3x2=66)432 
66x6=        396 


36x2=725)3625 
725x5=         3625. 


RTJ  L  E. 

1.  Separate  the  given  number  into  periods  of  two  figures 
each,  commencing  at  units. 

2.  Find  the  greatest  perfect  square  in  the  left  hand  period 
and  place  its  root  on  the  right  as  the  highest  order  of  the  root. 

3.  Subtract  the  square  of  the  root  figure  from  the  left  hand 
period,  and  to  the  remainder  annex  the  next  period  for  a 
dividend. 

4.  Double  the  part  of  the  root  already  found  for  a  trial 
divisor,  and  see  how  many  times  it  is  contained  in  the  divi- 
dend, exclusive  of  the  right  hand  figure,  and  write  the  quotient 
as  the  next  divisor  of  the  root,  and  also  at  the  right  of  the  trial 
divisor. 

5.  Multiply  the  divisor  thus  formed  by  the  figure  of  the 
root  last  found,  and  subtract  the  product  from  the  dividend. 


SQUARE     BOOT.  257 

6.  To  this  remainder  annex  the  next  period  for  the  next 
^dividend,  and  divide  the  same  by  twice  the  root  already  found, 

and  continue  in  this  manner  until  all  the  periods  are  used. 

Notes. — 1.  The  left  hand  period  often  contains  but  one 
figure. 

2.  Twice  the  root  already  found  is  called  the  trial  divisor, 
since  the  quotient  may  not  be  the  next  figure  of  the  root. 
The  quotient  may  be  too  large,  in  which  case  it  must  be  made 
less.     The  true  divisor  is  the  trial  divisor  with  the  figure  of 
the  root  found  annexed. 

3.  When  any  dividend  exclusive  of  its  right  hand  figure  is 
not  large  enough  to  contain  its  trial  divisor,  place  a  cipher  for 
the  next  figure  of  the  root,  and  double  the  root  thus  formed 
for  a  new  trial  divisor,  and  form  a  new  dividend  by  bringing 
down  the  next  period. 

4.  When  there  is  a  remainder  after  all  the  periods  are 
used,  annex  a  period  of  two  ciphers,  and  thus  continue  the 
operation  until  the  requisite  number  of  decimal  places  is  ob- 
tained.    In  this  case,  there  will  be  a  remainder,  how  far  soever 
the  operation  be  continued,  since  the  square  of  no  one  of  the 
nine  digits  ends  with  a  cipher. 

5.  The  square  root  of  a  common  fraction  may  be  found  by 
taking  the  root  of  both  terms,  when  they  are  perfect  squares. 
When  both  terms  of  a  fraction  are  not  perfect  squares,  and 
can  not  be  changed  to  perfect  squares,  the  root  of  the  fraction 
can  not  be  exactly  found.     The  approximate  root,  however, 
may  be  found  by  multiplying  the  numerator  of  the  fraction 
by  the  denominator,  and  extracting  the  root  of  the  product, 
and  dividing  the  result  by  the  denominator.     By  extracting 
the  root  to  decimal  places  the  error  may  be  further  lessened. 

G.  In  finding  the  square  root  of  a  decimal  or  a  mixed  deci- 
mal, commence  separating  into  periods  at  the  order  of  units 
for  the  whole  number,  and  at  the  order  of  tenths  for  the  deci- 
mal. If  there  be  an  odd  number  of 'decimal  places,  annex 
a  cipher. 

7.  Mixed  numbers  must  first  be  reduced  to  improper  frac- 
tions or  to  mixed  decimals. 


258  THE     RIGHT-ANGLED     TRIANGLE. 

3.  What  is  the  square  root  of  32041  ?  Ans.  179. 

4.  What  is  the  square  root  of  492804  ?  .Ans.  702. - 

5.  What  is  the  square  root  of  94249  ?  Ans.  307. 

6.  What  is  the  square  root  of  2  ?  Ans.  1.414 +  . 

7.  What  is  the  square  root  of  62.8  ? 

62.80(7.924,  Ans. 
7x7=       ^9 
7x2=14.9)13.80 
14.9  x. 9=          13.41 

7.9  x. 2=  15.82).3900 
15.82  x. 02=  _J3164 

7.92  x  2= 15.844^073600 

15.844  x. 004=  .063376 

.010224. 

8.  What  is  the  square  root  of  .0625  ?  u4rcs.  .25. 

9.  What  is  the  square  root  of  57600  ?  Ans.  240. 

10.  What  is  the  square  root  of  176.89  ? 

11.  What  is  the  square  root  of  -/-/•$  ?  Ans.  75F. 

12.  What  is  the  square  root  of  oW?  ?  Ans.  f  f. 

13.  What  is  the  square  root  of  30  £  ?  Ans.  51. 

14.  What  is  the  square  root  of  69£  ?  Ans.  8 J. 


THE    RIGHT-ANGLED    TRIANGLE. 

ART.  169.  An  angle  is  the  divergence  of  two  lines  meeting 
at  a  common  point. 

Angles  are  divided  into  three  classes ;  acute,  obtuse,  and 
right. 

The  annexed  figures  illustrate  the  three  kinds  of  angles. 


Acute.  Obtuse.  Eight  angle. 

A  triangle  is  a  figure  bounded  by  three  straight  lines.     It 
also  contains,  as  its  name  indicates,  three  angles. 

\ 


THE     BIGHT-ANGLED     TRIANGLE. 


259 


A  rigfy-angled  triangle  contains  a  right  angle. 

The  side  opposite  the  right  angle  is  called  the  hypotenuse, 

The  other  two  sides  are  called  the  base  and  perpendicular. 


Perpendicular.^ 


Base. 


It  is  an  established  theorem  that  the  square  of  the  hypot- 
enuse of  a  right-angled  triangle  is  equal  to  the  sum  of  the 
squares  of  the  other  two  sides. 

The  annexed  figure  illustrates  this  theorem  and  the  fol- 


lowing rules. 


KULE  1. — Extract  the  square  root  of  the  SUM  of  the  square 
of  the  base  and  the  square  of  the  perpendicular  ;  the  result 
be  the  HYPOTENUSE. 


260  CUBE     ROOT. 

KULE  2. — Extract  the  square  root  of  the  DIFFERENCE  'be- 
tween the  square  of  the  hypotenuse  and  the  square  of  the 
given  side;  the  result  will  be  the  other  side  required. 

E  x  a.  m  pies. 

1.  What  is   the  hypotenuse   of  a   right-angled    triangle 
whose  base  is  36  ft.  and  perpendicular  45  ft.?     Ans.  57.6  ft. 

2.  If  the  hypotenuse  of  a  right-angled  triangle  is  65  feet, 
and  the  base  52  feet,  what  is  the  perpendicular  ? 

Ans.  39  feet. 

3.  The  hypotenuse  of  a  right-angled   triangle  is  80  feet, 
and  the  perpendicular  48  feet,  what  is  the  base  ? 

Ans.  64  feet. 

4.  Two  ships  start  from  the  same  point  at  the  same  time. 
In  six  days,  one  has  sailed  500  miles  due  east,  and  the  other 
400  miles  due  north.     What  is  their  distance  apart  ? 

5.  How  far  from  the  base  of  a  building  must  a  ladder  100 
feet  in  length  be  placed  so  as  to  reach  a  window  60  feet  from 
the  ground  ?  Ans.  80  feet. 

flS.  A  room  is  32  feet  long  and  24  feet  wide  ;  what  is  the 
distance  between  the  opposite  corners  ?  Ans.  40  ft. 

7.  A  boy  in  flying  his  kite  let  out  500  feet  of  string  and 
then  found  that  the  distance  from  where  he  stood  to  a  point 
directly  under  the  kite  was  400  feet ;  how  high  was  the  kite  ? 

Ans.  300  feet. 


CUBE     ROOT. 

ART.  170.  The  Cube  Boot  of  a  number  is  a  number  which 
multiplied  by  itself  twice,  will  produce  the  given  number. 
Thus,  the  cube  root  of  64  is  4,  since  4  x  4  x  4=64. 

The  process  of  finding  the  cube  root  of  a  number  is  best 
understood,  as  in  square  root,  by  involving  a  number,  and  thus 
ascertaining  the  law  of  the  formation  of  the  power. 

The  first  nine  numbers  are, 

1,    2,      3,      4,        5,        6,        7,        8,        9, 
and  their  cubes, 

.1,     8,     27,     64,     125,     216,     343,     512,     729. 


CUBE     ROOT.  261 

From  which  it  is  seen  that  the  cube  of  any  number  composed  of 
one  order  of  figures  may  contain  one,  two,  or  three  orders. 

Conversely,  the  cube  root  of  any  number  composed  of  one, 
two,  or  three  orders,  is  composed  of  but  one  order. 

The  numbers  in  the  second  line  above  are  the  only  perfect 
cubes  below  1000. 

Again,  103=1000  and  903=729000.  From  which  it  is  seen 
that  the  cube  of  tens  gives  no  order  below  thousands,  or  above 
hundreds  of  thousands.  In  the  same  manner  it  may  be  shown 
that  the  cube  of  any  number  must  contain  at  least  three  times 
as  many  orders,  less  two,  as  the  number  cubed.  Thus  the  cube 
of  any  number  composed  of  four  orders  must  contain  either 
ten,  eleven,  or  twelve  figures. 

Let  us  now  involve  a  number  composed  of  two  orders  — 
tens  and  units  —  to  the  third  power,  and  observe  the  law  of 
formation. 

54?=  503  +  3  x  50'  x  4+3  x  50  x  42  +  43=  125000  +  30000+2400 
+  64=157464. 

By  using  algebraic  symbols,  it  may  be  rigidly  shown  that 
what  is  true  of  the  above  number,  is  true  of  any  number  com- 
posed of  tens  and  units  ;  that  is, 

The  cube  of  any  number  composed  of  tens  and  units  is 
equal  to  the  cube  of  the  tens,  plus  three  times  the  product  of 
the  square  of  the  tens  by  the  units,  plus  three  times  the  product 
of  the  tens  by  the  square  of  the  units,  plus  the  cube  of  the  units. 

Let  us  now  proceed  to  determine  a  process  by  which  the 
cube  root  of  a  number  may  be  found. 

Ex.  1.  What  is  the  cube  root  of  157465  ? 

54  1574644154 

>4  5'=    125         " 


216  5s  x  3=75  324 

270  54'  =  157464 

2916 
54 


11664 
14580 
157464 


262  CUBE     ROOT. 

Explanation. — Since  157464  is  composed  of  six  orders,  the 
root  will  be  composed  of  two,  and  since  the  cube  of  tens  give 
no  order  below  thousands,  we  separate  the  number  into  periods 
of  three  figures  each  by  placing  a  dot  over  units,  and  another 
over  thousands.  Now,  according  to  principles  above  explained, 
157  must  contain  the  cube  of  the  ten's  figure  of  the  root.  The 
greatest  cube  in  157  is  125,  the  cube  root  of  which  is  5. 
Place  5  for  the  ten's  figure  of  the  root.  Subtract  the  cube  of 
5  from  157,  and  annex  4  of  the  next  period  to  the  remainder, 
giving  324.  Now  three  times  the  product  of  the  square  of  the 
tens  by  the  units  must  be  found  in  324,  since  the  square  of  tens 
gives  no  order  below  hundreds. 

Square  5  tens  and  multiply  the  result  by  3  for  a  trial  divi- 
sor to  find  the  next  root  figure.  Place  the  quotient  below  the 
order  in  the  root.  It  may  be  too  large,  since  three  times  the 
product  of  the  tens  by  the  square  of  the  units  may  give  orders 
above  tens,  thus  forming  a  part  of  324,  cube  54,  and  since  the 
result  is  not  greater  than  157464,  place  4  for  the  unit's  figure 
of  the  root. 

Ex.  2.  What  is  the  cube  root  of  34328125  ? 
33  32 


33=        27 
W  "~64 


34328125325 
35 


99              96  3'x3=     27)73__ 

iSr    TOM  32-    ^™- 

32  32' x  3=3072)15601 

3267"       "2048  325°=         34328125. 
3267          3072 
"35937        32768 


1.  Separate  the  given  numbers  into  periods  of  three  figures 
each,  commencing  at  units. 

2.  Find  the  greatest  perfect  cube  in  the  left  hand  period, 
and  place  its  root  on  the  right  as  the  highest  order  of  the  root. 

3.  Subtract  the  cube  of  the  root  figure  from  the  left  hand 
period,  and  to  the  remainder  annex  the  first  figure  of  the  next 
period  for  a  dividend. 


CUBE     BOOT.  263 

4.  Take  three  times  the  square  of  the  root  figure  now  found 
for  a  trial  divisor,  and  place  the  number  of  times  it  is  con- 
tained in  the  dividend,  for  the  next  figure  of  the  root.      Cube 
the  root  now  found,  and  if  the  result  is  less  than  the  first  tiuo 
periods  of  the  given  number,  bring  down  the  first  figure  of  the 
next  period  for  a  neio  dividend  ;  if,  however,  the  cube  is 
greater  than  the  first  two  periods,  diminish  the  last  root  figure 
by  I. 

5.  Take  three  times  the  square  of  the  root  now  found  for 
a  new  trial  divisor,  and  place  the  number  of  times  it  is  con- 
tained in  the  new  dividend  for  the  third  figure  of  the  root. 
Cube  the  three  figures  of  the  root,  and  subtract  the  result  from 
the  first  three  periods  of  the  given  number.      Continue  the 
operation  in  a  similar  manner  until  all  the  periods  are  used. 

Notes. — 1.  When  any  dividend  is  not  large  enough  to  con- 
tain its  trial  divisor,  place  a  cipher  for  the  next  figure  of  the 
root,  and  take  three  times  the  square  of  the  root  thus  formed 
for  a  new  trial  divisor.  Form  a  new  dividend  by  bringing 
down  the  remaining  two  figures  of  the  period,  and  the  first 
figure  of  the  next  period. 

2.  When  there  is  a  remainder  after  all  the  periods  are  used, 
annex  periods  of  ciphers  and  continue  the  operation  until  the 
requisite  number*  of  decimal  places  is  obtained. 

3.  Extract  the  cube  root  of  both  terms  of  a  common  frac- 
tion, when  they  are  perfect  powers  ;  otherwise  multiply  the 
numerator  by  the  square  of  the  denominator,  and  divide  the 
root  of  the  product  by  the  denominator.    The  result  will  be  the 
root  with  an  error,  less  than  one  divided  by  the  denominator. 

4.  In  extracting  the  cube  root  of  decimals  or  mixed  deci- 
mals, ciphers  must  be  added,  to  fill  the  periods. 

Kxamples. 

1.  What  is  the  cube  root  of  912673  ?  Ans.  97. 

2.  What  is  the  cube  root  of  128024064  ?  Ans.  504. 

3.  What  is  the  cube  root  of  48228544  ?  Ans.  364. 

4.  What  is  the  cube  root  of  3048625  ?  Ans.  145. 

5.  What  is  the  cube  root  of  39TVj  ?  -4»«-  3|. 


264  ARITHMETICAL     PROGRESSION. 

6.  What  is  the  cube  root  of  .000097336  ?  Ana.  .046. 

7.  What  is  the  cube  root  of  llf  f  ?  Ans.  2^  ? 

8.  What  is  the  cube  root  of  7f  H*  ?  ^s-  aV 

9.  What  is  the  cube  root  of  14  ?  ^/is.  2.42  +  . 
10.  What  is  the  cube  root  of  .015625  ?  Ans.  .25. 


ARITHMETICAL    PROG-RESSIO1ST. 

ART.  171.  When  several  numbers  are  so  arranged  as  to 
increase  or  decrease  in  regular  order  by  a  common  difference, 
they  are  said  to  be  in  arithmetical  progression. 

When  they  increase  by  the  addition  of  a  constant  number, 
•it  is  called  an  ascending  series,  e.  g.,  1,  3,  5,  7,  9,  11,  13,  &c. 

When  they  decrease  by  the  subtraction  of  a  constant  num- 
ber, it  is  called  a  descending  series,  e.  g.,  19,  16,  13,  10,  &c. 

The  numbers  are  called  terms,  the  first  and  last  being 
called  extremes,  and  the  intermediate  terms  the  means. 

In  arithmetical  progression  there  are  five  quantities  so 
related  to  each  other,  that  any  three  of  them  being  given,  the 
remaining  two  may  be  found.  This  fact  gives  rise  to  twenty 
different  cases  or  problems,  only  six  of  which  will  here  be  given. 
These  five  quantities  in  the  formulas  expressing  their  rela- 
tion, are  represented  as  follows  : 

a  =  The  first  term. 

I  =  The  last  term. 

d  =  The  common  difference. 

n  =  The  number  of  terms. 

s  =  The  sum  of  all  the  terms. 

FORMULAS. 

(1),  a,  d  and  n  being  given,   l=a±(n—  Y)d. 
(2),  a,n    '     I     "         "      d=^. 


(3),  a.  d    "    I     "         "      n=t-a+l. 
(4),  a,  n    "    I 
(5),  d,n   "    s 


"          " 


,     ,  . 

(6),  a,  d   '     n     "         "      s=i«[2a±(»-l)d]. 


ARITHMETICAL     PROGRESSION.  265 

The  interpretation  of  these  formulas  for  those  not  familiar 
with  algebraic  expressions,  will  furnish  the  following  rules. 
The  student  will  be  able  to  select  the  proper  rule  for  any  par- 
ticular case  by  noting  carefully  which  three  of  the  five  quan- 
tities are  given,  and  which  is  required. 

(1).  The  first  term,  common  difference,  and  number  of 
terms  being  given  to  find  the  last  term. 

EULE. — Multiply  the  common  difference  by  the  number  of 
terms,  less  one,  and  add  the  product  to  the  first  term,  if  the 
series-  be  ASCENDING,  but  subtract  it  from  it,  if  the  series  be 

DESCENDING. 

(2).  The  first  term,  number  of  terms,  and  last  term  being 
given  to  find  the  common  difference. 

KULE. — Divide  the  difference  of  the  extremes  by  the  num- 
ber of  terms ,  less  one. 

(3).  The  first  term,  common  difference,  and  last  term  being 
given  to  find  the  number  of  terms. 

KULE. — Divide  the  difference  of  the  extremes  by  the  com- 
mon difference,  and  add  1  to  the  quotient. 

(4).  The  first  term,  number  of  terms,  and  last  term  being 
given  to  find  the  sum  of  all  the  terms. 

KULE. — Multiply  half  the  sum  of  the  extremes  by  the  num- 
ber of  terms. 

(5).  The  common  difference,  number  of  terms,  and  sum  of 
all  the  terms  being  given  to  find  the  first  term. 

KULE. — Divide  the  sum  of  the  terms  by  the  number  of 
terms  ;  subtract  from  the  quotient,  if  the  series  be  ascending, 
otherwise  add  to  it  half  the  product  of  the  common  difference 
into  the  number  of  terms,  less  one. 

(6).  The  first  term,  common  difference,  and  number  of 
terms  being  given  to  find  the  sum  of  all  the  terms. 

KULE. — Add  to  twice  the  first  term,  if  the  series  be  ascend- 
ing; otherwise  subtract  from  it  the  product  of  the  common 
difference  into  the  number  of  terms,  less  one  ;  multiply  the 
sum  or  difference  by  half  the  number  of  terms. 


266  ARITHMETICAL      PROGRESSION. 

Id  'x.  a,  m.  pies. 

1.  A  laborer  agreed  to  dig  a  well  100  feet  deep,  for  which 
he  was  to  receive  1  cent  for  the  first  foot,  5  cents  for  the  second 
and  so  on  increasing  the  price  4  cents  per  foot  for  the  entire 
depth.     What  would  he  get  for  the  last  foot  ? 

Ans.   $3.97. 

2.  If  a  man  begin  by  lifting  200  Ibs.,  and  make  equal  ad- 
ditions to  the  weight  daily  for  a  year  of  365  days,  what  must 
be  the  daily  additions  to  reach  800  Ibs.  at  the  end  of  the  year? 

Ans.  Iff-  Ibs. 

Secondly.    With  what  weight  must  he  begin,  so  that  the 
daily  additions  may  be  two  pounds  ?  Ans.  72  Ibs. 

Thirdly.     If  he  begin  with  200  Ibs.,  and  add  1 J  Ibs.  daily, 
how  many  days  would  it  require  to  reach  800  Ibs. 

Ans.  401  days. 

3.  How  many  strokes  does  the  hammer  of  a  clock  make  in 
12  hours  ?  Ans.  78. 

4.  If  100  stakes  bo  set  in  a  straight  line  10  feet  apart,  how 
much  twine  will  it  require  to  connect  the  first  one  in  the  line 
with  each  of  the  others  separately  ?  Ans.  49500  feet. 

5.  A  man  agreed  to  contribute  for  a  benevolent  object  one 
cent  the  first  day,  two  cents  the  second  day,  three  cents  the 
third  day,  and  so  on  through  the  year  of  365  days.     What 
was  the  amount  of  his  donation  ?  Ans.  $667.95. 

6.  A  note  was  given  for  $1000,  with  interest  payable  an- 
nually, at  7%.      Nothing  having  been  paid  for  ten  years,  how 
much  did  the  total  amount  of  interest  due  exceed  the  simple 
interest  of  the  principal  ?     See  Art.  100.          Ans.  $220.50. 

7.  If  a  note  for  §2000,  drawing  interest  at  6^  per  annum, 
run  10  yrs.  3  mo.  9  d.  with  nothing  paid,  how  much  would 
the  condition  of  making  the  "  interest  payable  semi-annually" 
increase  the  amount  due  ?  Ans.  $361.80. 


GEOMETRICAL     PROGRESSION.  267 


GEOMETRICAL    PROGRESSION. 

ART.  172.  A  geometrical  progression  is  such  a  series  of 
numbers,  that  each  term  after  the  first  shall  be  the  product 
of  the  preceding  term  and  a  constant  multiplier,  called  the 
common  ratio. 

The  progression  is  ascending  or  descending,  according  as 
the  ratio  is  greater  or  less  than  unity. 

In  geometrical  progression,  as  in  arithmetical  progression, 
there  are  five  quantities  so  related  to  each  other,  that  any 
three  of  them  being  given  the  remaining  two  may  be  found. 
Of  the  twenty  cases  arising  therefrom  only  four  will  here  be 
noticed. 

In  the  formulas  expressing  the  relation  of  the  five  quan- 
tities referred  to  above,  they  are  represented  as  follows : 
a  =•  The  first  term. 
I  =  The  last  term. 
r  =  The  common  ratio. 
n  =  The  number  of  terms. 
s  =  The  sum  of  all  the  terms. 

FORMULAS. 

(1,)  a,  r  and  n  being  given,  ?=arn~~1. 

(2,)  ?,  r  and  n      "          "       a=^. 
;     (3,)  a,  I  and  r      «          «       s=^. 

(4;)  a,  r  and  n      "          "       s  =  *^-. 

These  formulas  are  equivalent  to  the  following  rules  : 
(1.)  The  first  term,  common  ratio,  and  number  of  terms 
being  given  to  find  the  last  term. 

RULE. — JRaise  the  common  ratio  to  a  power  whose  degree 
is  one  less  than  the  number  of  terms,  and  multiply  it  by  the 
first  term. 

(2.)  The  last  term,  common  ratio,  and  number  of  terms 
being  given  to  find  the  first  term. 


268  GEOMETRICAL     PROGRESSION. 

RULE. — Raise  the  common  ratio  to  a  power  whose  degree, 
is  one  less  than  the  number  of  terms,  and  divide  the  last  term 
by  it. 

(3.)  The  first  term,  last  term,  and  common  ratio  being 
given  to  find  the  sum  of  all  the  terms. 

RULE. — From  the  product  of  the  last  term  into  the  ratio, 
subtract  the  first  term;  then  divide  the  remainder  by  the  ratio 
less  one. 

(4.)  The  first  term,  common  ratio,  and  number  of  terms 
being  given  to  find  the  sum  of  all  the  terms. 

RULE. — From  the  power  of  the  ratio  whose  degree  is  the 
number  of  terms,  subtract  one;  divide  the  remainder  by  the 
common  ratio  less  one,  and  multiply  the  quotient  by  the  first 
term. 

REMARK. — It  is  sometimes  convenient  in  working  problems 
to  transpose  a  descending  series  so  as  to  make  it  ascending,  the 
last  term  of  the  first  series  becoming  the  first  term  in  the  new. 
In  that  case  the  new  ratio  would  be  the  reciprocal  of  the  old, 
i.  e.,  unity  divided  by  that  ratio,  e.  g.,  ±  would  become  3,  | 
would  become  4,  and  so  on. 

Infinite  Series. 

ART.  173,  If  the  number  of  terms  in  a  descending  geomet- 
rical series  be  infinite,  the  last  term  will  be  0. 

It  does  not,  however,  follow  that,  because  the  number  of 
terms  is  infinite,  the  sum  of  those  terms  must  be  infinite,  for 
if  we  apply  formula  (3)  making  the  last  term  0,  we  shall  find 
the  sum  of  an  infinite  decreasing  series  to  be  the  first  term 
divided  by  the  difference  between  the  common  ratio  and  unity, 

Examples. 

1.  A  man  offered  to  purchase  10  cows,  paying  for  the  first 
5  cents,  for  the  second  15  cents,  and  so  on  tripling  the  amount 
for  each  succeeding  cow.  What  would  the  last  one  cost  him, 
and  what  would  the  whole  cost  him  ? 

Ans.  The  last  would  cost  $984.15. 
u       "     whole        "     $1476.20. 


GEOMETRICAL     PROGRESSION.  269 

2.  If  the  first  term  be  100,  the  common  ratio  1.06,  and  the 
number  of  terms  5,  what  is  the  last  term  ?    Ans.  126.2477. 

NOTE. — As  the  principles  of  arithmetical  progression  may 
be  applied  with  advantage  to  the  computation  of  annual  in- 
terest, so  may  those  of  geometrical  progression  in  computing 
compound  interest.  When  thus  applied  the  principal  is  the 
first  term,  the  amount  the  last  term,  the  number  of  regular 
intervals,  at  the  end  of  which  the  interest  is  to  be  com- 
pounded, one  less  than  the  number  of  terms,  and  the  amount 
of  one  dollar  for  one  of  those  intervals  the  common  ratio.  To 
find  the  different  powers  of  the  ratio,  the  table  on  pages  132 
and  133  may  be  used,  the  number  in  the  column  of  years  in- 
dicating the  degree  of  the  power ;  e.  g.,  the  50th  power  of 
1.03i  is  5.58492686. 

3.  What  is  the  amount  of  §100  for  50  years  at  10  %  com- 
pound interest  ?  Ans.  $11739.09. 

4.  If  a  man  beginning  at  the  age  of  21,  at  the  end  of  each 
year  pu's  $100  at  compound  interest,  what  will  these  sums 
amount  to  when  he  is  50  years  old  ?  Ans.  $7363.98. 

5.  A  gentleman  offered  for  sale  a  lot  of  ten  acres  on  the 
following  terms  :  one  mill  for  the  first  acre,  one  cent  for  the 
second,  one  dime  for  the  third,  and  so  on  in  geometrical  pro- 
gression.    What  was  his  price  for  the  whole  ? 

Ans.  $1111111.111. 

6.  What  is  the  sum  of  the  series  T37,  T^,  To3oo?  &c->  or 
.333,  &c.j  carried  to  infinity  ?  Ans.  \. 

7.  What  common  fraction  is  equivalent  to  the  repetend 
.7777,  &c.  ?  Ans.  J. 

8.  At  12  o'clock  the  hour  and  minute  hands  of  a  clock  are 
together.     In  what  time  will  they  b3  together  again  ? 

SOLUTION*. — When  the  minute  hand  has  performed  one  entire  revolution 
around  the  face  of  the  clock,  the  hour  hand  will  be  yV  of  a  revolution  in  advance. 
When  the  minute  hand  shall  have  gone  over  this  rV,  the  hour  hand  will  still  be 
yV  of  that  twelfth  in  advance,  or  y^y  of  an  entire  revolution.  When  the  minute 
hand  shall  have  reached  that  point,  the  hour  hand  will  be  y  2  of>  TTT  in  advance, 
and  so  the  comparison  of  their  relative  position  may  be  supposed  to  be  made  an 
infinite  number  of  times.  It  is  evident  that  for  the  minute  hand  to  overtake  the 
hour  hand,  it  must  perform  as  many  revolutions  (andl  hence  take  as  many  hours) 


270  MENSURATION. 

as  would  be  the  sum  of  the  series  1,  yV,  74 T»  TTaTi  &c.,  continued  to  infinity 
equal  to  ITT  hours.  "With  the  above  reasoning  one  might  almost  believe  that 
the  hour  hand  would  always  be  ahead,  bat  as  a  matter  of  fact  we  know  that  the 
minute  hand  does  overtake  and  pass  the  hour  hand,  and  therefore  at  some  point 
the  distance  between  the  two  must  be  nothing.  Farthermore,  as  the  series  above 
represents  the  successive  distances  apart  in  their  actual  progress,  we  have  from 
this  case  conclusive  proof  that  the  last  term  of  an  infinite  decreasing  geometrical 
series  is  absolutely  nothing. 

9.  If  an  ivory  ball  is  let  fall  upon  a  marble  slab,  from  a 
height  of  10  feet,  and  it  rebounds  9  feet,  falling  again  it  re- 
bounds 8.1  feet,  and  so  continues  always  rebounding  T9¥  of  the 
distance  through  which  it  fell  last,  will  it  ever  come  to  rest, 
and  if  so,  through  what  space  will  it  have  passed  ? 

Ans.  It  would  pass  through  190  feet. 

10.  If  the  banking  law  of  Illinois  allows  the  State  Auditor 
to  issue  to  any  banker  depositing  State  Stocks,  90  per  cent,  of 
the  par  value  of  those  stocks  in  circulating  bank  notes,  without 
farther  restriction,   what  is  the  amount  of  Stocks  a  banker 
could  so  put  on  deposit  with  only  $10000  Cash  Capital,  if  he 
continue  to  re-invest  the  bank  notes  for  other  Stocks  both  at 
par,  until  he  should  have  nothing  to  re-invest  ?   If  the  Stocks 
draw  6  %  interest,  what  dividend  does  he  realize  on  his  capital  ? 

Ans.  to  the  first  $100.000. 

second  60  %  per  annum. 


MENSURATION. 

ART.  174,  A  point  has  neither  length,  breadth,  nor  thick- 
ness, but  position  only. 

A  line  has  length  without  breadth  or  thickness,  and  may 
be  straight  or  curved. 

A  surface,  has  length  and  breadth  without  thickness,  and 
may  be  plain  or  curved. 

A  solid  has  length,  breadth,  and  thickness. 

An  angle  is  the  divergence  of  two  straight  lines  from  a 
common  point.  When  the  divergence  is  equal  to  that  made 


MENSURATION.  271 

by  a  straight  line  and  one  perpendicular  to  it,  it  is  called  a 
right  angle,  and  its  measure  is  90  degrees  (90°).  A  less  di- 
vergence forms  an  acute  angle,  and  a  greater  an  obtuse  angle. 

The  area  of  a  figure  is  its  quantity  of  surface,  and  is 
measured  by  the  product  of  the  linear  dimensions  of  length 
and  breadth,  which  will  give  the  number  of  square  units  of  the 
same  denomination  covering  an  equivalent  surface. 

EEMARK. — The  only  difficulty  then  in  computing  the  area  of  any  figure  is  to 
find  the  linear  dimensions  of  its  average  length  and  breadth,  or  those  of  another 
figure  known  to  be  of  equal  area.  Take  for  example  the  "  quadrature  of  the 
circle."  It  can  easily  be  proven  that  the  area  of  a  circle  is  equal  to  the  area  of  a 
rectilinear  figure,  with  a  length  equal  to  the  circumference  of  the  circle,  and  a 
breadth  equal  to  half  the  radius ;  but  as  our  system  of  notation  -will  not  express 
the  exact  length  of  the  radius  for  a  given  circumference,  nor  the  exact  length  of 
the  circumference  for  a  given  radius,  the  problem  will  not  admit  of  an  exact  solu- 
tion, though  the  approximation  may  be  carried  to  an  indefinite  extent. 

The  solidity  or  volume  of  a  solid  or  body  is  the  quantity 
of  space  which  it  occupies,  and  is  measured  by  the  product  of 
the  three  linear  dimensions  of  length,  breadth,  and  thickness, 
which  will  give  the  number  of  cubic  units  of  the  same  deno- 
mination occupying  an  equivalent  space. 

A  rectilinear  figure,  or  polygon,  is  a  plane  figure  bounded 
by  straight  lines.  A  polygon  of  three  sides  is  called  a  triangle, 
of  four  sides  a  quadrilateral,  of  five  a  pentagon,  of  six  a  hexa- 
gon, and  so  on. 

A  regular  polygon  is  one  whose  sides  and  angles  are  equal. 

A  trapezium  is  a  quadrilateral  which  has  no  two  sides 
parallel. 

A  trapezoid  is  a  quadrilateral  which  has  only  two  sides 
parallel. 

A  parallelogram  is  a  quadrilateral  whose  opposite  sides 
are  equal  and  parallel. 

The  altitude  of  a  parallelogram  or  trapezoid  is  the  perpen- 
dicular distance  between  the  parallel  sides. 
.     A  rectangle  is  a  right-angled  parallelogram. 

A  square  is  an  equilateral  rectangle. 

A  rhombus  is  an  equilateral  parallelogram  with  only  its 
opposite  angles  equal. 


272  TRIANGLES. 

A  rhomboid  is  a  parallelogram  neither  equilateral  nor 
equiangular. 

Similar  figures  are  those  whose  corresponding  angles  are 
equal,  and  the  sides  about  the  equal  angles  proportional. 

The  areas  of  similar  figures  are  to  each  other  as  the  squares 
of  their  corresponding  linear  dimensions,  and  the  volumes  of 
similar  solids  are  to  each  other  as  the  cubes  of  their  corre- 
sponding linear  dimensions. 


TRIANGLES. 

ART.  175-  In  computing  the  area  of  a  triangle,  either  side 
may  he  assumed  as  the  base,  and  the  altitude  will  be  the  per- 
pendicular let  fall  from  the  vertex  of  the  angle  opposite  upon 
the  base,  or  base  produced  if  necessary. 

To  find  the  area  of  a  triangle. 

KULE. — Multiply  the  base  by  half  the  altitude,  and  the 
product  will  be  the  area;  or 

Take  half  the  sum  of  the  three  sides,  and  from  this  sub- 
tract each  side  separately;  then  multiply  together  the  half 
sum  and  the  three  remainders,  and  the  square  root  of  the  pro- 
duct will  be  the  area. 

IE  x  a  m  pies. 

1.  How  many  square  yards  in  a  piece  of  ground  of  trian- 
gular shape,  one  side  measuring  50  yards,  and  the  shortest 
distance  from  this  side  to  the  opposite  angle  being  24  yards  ? 

Ans.  600  sq.  yds. 

2.  The  three  sides  of  a  triangle  measure  respectively  10, 
12,  and  14  feet  ;  what  is  the  area  ?          Ans.  58.7878  sq,  ft. 

3.  How  much  greater  would  be  the  area  if  we  double  the 
linear  dimensions  in  the  last  example  !        Ans.  Four  times. 

4.  What  should  be  the  dimensions  of  a  triangle  similar  to 
the  one  proposed  in  example  1,  to  make  the  area  5400  s.q. 
yards  instead  of  GOO  ?  Ans.    The  base  150  yds. 

The  altitude  72  yds. 

5.  If  one  side  of  a  field  containing  50  acres  is  50  rods, 


&c.       273 

•what  must  be  the  length  of  the  corresponding  side  of  a  field 
of  similar  shape  to  contain  112|  acres  ?  Ans.  75  rods. 

6.  The  area  of  a  certain  triangular  field  is  3f  acres,  and 
one  of  its  sides  is  37 1  rods  long  ;  what  is  the  length  of  a  per- 
pendicular from  the  opposite  corner  ?  Ans.  32  rods. 

7.  What  is  the  side  of  a  square  containing  the  same  area 
as  a  triangle  whose  base  is  36.1  feet,  and  altitude  5  feet  ? 

Ans.  9^  feet. 


QUADRILATERALS,    PENTAGONS,    &c. 

ART.  176.  (1.)  To  find  the  area  of  any  quadrilateral  having 
two  sides  parallel. 

RULE. — Multiply  half  the  sum  of  the  two  parallel  sides  by 
the  altitude,  or  perpendicular  distance  between  those  sides, 
and  the  product  ivill  be  the  area.  * 

NOTE. — This  rule  is  equally  applicable  to  the  square,  rect- 
angle, rhombus,  rhomboid,  and  trapezoid.  If  the  parallel  sides 
are  equal,  the  half  sum  would  be  equal  to  one  of  them. 

(2.)  To  find  the  area  of  a  regular  polygon. 

RULE. — Multiply  the  sum  of  the  sides  or  perimeter  by  half 
the  perpendicular  let  fall  from  the  center  upon  one  of  its  sides. 

Or, 

Multiply  the  square  of  one  of  the  sides  by  the  appropriate 
number  as  given  in  the  following 

TABLE. 


Triangle, 

.433013 

Octagon, 

4.828427 

Square, 

1.000000 

Nonagon, 

6.181824 

Pentagon, 

1.720477 

Decagon, 

'-  7.694209 

Hexagon, 

2.598076 

Undecagon, 

9.365640 

Heptagon, 

3.633912 

Dodecagon, 

11.196152 

(3.)  To  find  the  area  of  an  irregular  polygon  of  four  or 
more  sides. 

RULE. — Divide  the  figure  into  triangles  by  diagonals  con- 
necting some  one  angular  point  with  each  of  the  others;  com- 
pute the  area  of  each  triangle,  and  their  sum  will  be  the  area 

required. 

IS 


274  CIRCLES. 

Examples. 

1.  How  many  square  feet  in  a  board  14  feet  long  and  10 
inches  wide  ?  Ans,  11 1  sq.  ft. 

2.  How  many  square  feet  in  a  board  14  feet  long,  it  being 
15  inches  wide  at  one  end,  and  9  inches  at  the  other  ? 

Ans.  14  sq.  ft. 

3.  If  the  same  board  be  cut  in  two  in  the  middle,  making 
each  piece  7  feet  long,  how  much  more  would  one  piece  con- 
tain than  the  other  ?  Ans.  If  sq.  ft. 

4.  If  the  parallel  sides  of  a  trapezoid  are  48  and  52  feet, 
and  the  perpendicular  breadth  17  feet,  what  is  the  area  ? 

Ans.  850  sq.  ft. 

5.  What  is  the  area  of  a  regular  decagon,  one  of  its  sides 
being  10  feet,  and  the  perpendicular  let  fall  from  the  center 
upon  one  of  the  sides  being  15.3884  feet  ? 

Ans.  7G9.420  sq.  ft. 

6.  What  is  the  area  of  a  regular  pentagon,  one  of  its  sides 
being  20  rods  ?  Ans.  688.191  sq.  rods. 

7.  What  must  be  the  side  of  a  regular  octagonal  field  to 
contain  3  acres,  2  roods,  14  rods,  19  yards  ?    Ans.  60  yards. 

8.  The  sides  of  a  certain  trapezium  measure  10,  12,  14; 
and  16  rods  respectively,  and  the  diagonal  which  forms  a  tri- 
angle with  the  first  two  sides  named  18  rods,  what  is  the  area  ? 

Ans.  1  acre  3.9  rods. 

9.  How  much  more  fencing  will  it  require  to  enclose  an 
acre  in  the  form  of  a  square  than  in  the  form  of  a  hexagon  ? 

Ans.  3.51  rods. 


CIRCLES. 

ART.  177.  The  ratio  between  the  diameter  and  circum- 
ference is  an  important  number  in  problems  relating  to  the 
circle,  and  its  approximate  value  should  be  retained  in  tlae 
memory.  That  ratio  is  very  nearly  equivalent  to  the  fraction 
35  s?  which  may  easily  be  remembered  from  its  containing  the 
first  three  odd  numbers  each  repeated,  and  found  in  their 


CIRCLES.  275 

natural  order,  if  we  read  the  denominator  first.  If  expressed 
decimally,  and  the  approximation  be  earned  to  thirty  places, 
we  have  the  following,  3.14159265358979323846264338328. 

(1.)  To  find  the  circumference  of  a  circle  whose  diameter 
is  known. 

RULE. — Multiply  the  diameter  by  £ff  or  3.1416. 

(2.)  To  find  the  diameter,  the  circumference  being  known. 

RULE. — Divide  the  circumference  by  fff  or  3.1416. 

(3.)  To  find  the  area  of  a  circle,  the  diameter  being  known. 

RULE. — Multiply  the  square  of  half  the  diameter  by  £f  f 
or  3.1416. 

(4.)  To  find  the  area  of  a  circle,  the  circumference  being 
known. 

RUL"E. — Divide  the  square  of  half  the  circumference  by 
f  f  f  or  3.1416. 

(5.)  To  find  the  area  of  a  circle,  the  circumference  and 
diameter  both  being  known. 

RULE. — Multiply  the  circumference  by  one  fourth  of  the 
diameter.  See  Art.  174,  Remark. 

(6.)  To  find  the  diameter  or  circumference  of  a  circle,  the 
area  being  known. 

RULE. — Divide  the  area  by  ff I  or  3.1416,  the  square  root 
of  the  quotient  will  be  equal  to  half  the  diameter;  and  the 
diameter  multiplied  by  f  *-}  or  3.1416,  will  equal  the  circum- 
ference. 

(7.)  To  find  the  side  of  the  largest  square  that  can  be  in- 
scribed in  a  circle. 

RULE. — Multiply  the  radius  by  the  square  root  of  two  (^2). 

(8.)  To  find  the  side  of  the  largest  equilateral  triangle  that 
can  be  inscribed  in  a  circle. 

RULE.-— Multiply  the  radius  by  the  square  root  of  three  (^3). 

Note. — The  side  of  an  inscribed  hexagon  is  equal  to  the 
radius. 

"Examples. 

1.  Suppose  the  earth  to  be  distant  from  the  sun  95  millions 
of  miles,  and  to  revolve  in  a  circular  orbit,  how  far  "does  it 
move  in  an  hour  ?  Ans.  68093  miles. 


276  ELLIPSE. 

2.  What  is  the  diameter  of  a  peach  which  measures  12 
inches  in  circumference  ?  Ans.  3.82  inches. 

3.  What  must  be  the  inside  measure  of  a  square  box  to 
exactly  contain  a  globe  56  inches  in  circumference  ? 

Ans.  17.825+  in.  sq. 

4.  If  a  horse  be  tied  to  a  stake  in  a  meadow,  with  a  halter 
20  feet  long,  upon  how  many  square  yards  can  he  feed  ? 

Ans.  139.626  + . 

5.  If  a  circular  fish  pond  is  to  be  laid  out  containing  just 
half  an  acre,  what  must  be  the  radius  or  length  of  the  cord 
needed  to  describe  the  circle  ?  Ans.  27.75  yds. 

6.  What  is  the  area  of  a  ring  formed  by  two  circles  whose 
diameters  are  9  and  13  inches  ?  Ans.  69.1152  sq.  in. 

7.  How  large  a  square  stick  may  be  hewn  from  a  piece  of 
round  timber  109  inches  in  circumference  ?  Ans.  22.5  in.  sq. 


ELLIPSE. 

ART.  178.  To  find  the  area  of  an  ellipse  the  two  diameters 
being  given. 

RULE. — Multiply  the  two  diameters  together,  then  multiply 
one  fourth  of  this  product  by  ^ff  or  3.1416. 

Examples. 

1.  What  is  the  area  of  an  ellipse  whose  two  diameters  are 
18  and  24  feet  ?  Ans.  339.2928  sq.  ft. 

-    2.  What  is  the  area  of  an  ellipse  whose  longest  diameter  is 
20  feet,  and  shortest  15  feet  ?  Ans.  235.62  sq.  ft. 


MENSURATION    OF    SOLIDS. 

PRISMS    AND    CYLINDERS. 

ART.  179.  A  prism  is  a  solid  whose  sides  or  faces  are  par- 
allelograms and  whose  ends  or  bases  are  equal  and  parallel 
polygons.  A  prism  is  triangular,  quadrangular,  pentagonal, 
&c.,  according  as  its  bases  are  triangles,  squares,  or  penta- 
gons, &c. 

A  parallelepiped  is  a  prism  whose  bases  are  parallelograms. 


PYRAMIDS     AND     CONES.  277 

A  cylinder  is  a  solid  resembling  a  prism,  but  having,  in- 
stead of  polygons,  for  its  bases,  equal  parallel  circles  or  other 
figures  more  or  less  elliptical  ;  its  surface  otherwise  being  uni- 
formly curved  instead  of  being  made  up  of  several  plane  faces. 

The  lateral  or  convex  surface  of  a  prism  or  cylinder  does 
not  include  the  two  ends  or  bases. 

A  solid  is  said  to  be  right  when  its  axis  or  general  direc- 
tion is  at  right  angles  with  the  base  ;  otherwise  it  is  oblique. 

To  find  the  entire  surface  of  a  right  prism  or  right  cylinder. 

RULE. — Multiply  the  perimeter  or  circumference  of  the  base 
by  the  height ,  and  to  the  product  add  the  area  of  the  two  bases. 

To  find  the  solidity  of  a  prism  or  cylinder. 

RULE. — Multiply  the  area  of  the  base  by  the  perpendicular 
height. 

NOTE. — In  this  case  it  matters  not  whether  the  solid  be 
right  or  oblique. 

E  x:  a  m  pies. 

1.  What  is  the  extent  of  surface  of  a  rignt  cylinder  10  feet 
long,  the  diameter  of  the  base  being  2  feet  ? 

Ans.  69.1152  sq.  ft. 

2.  What  is  the  solidity  of  a  triangular  prism  whose  per- 
pendicular height  is  150  feet,  the  sides  of  the  base  being  60, 
80,  and  100  feet  ?  Ans.  360000  en.  ft. 


PYRAMIDS    AND    CONES. 

ART.  180.  A  pyramid  is  a  solid  whose  base  is  a  polygon, 
and  whose  sides  are  triangles  meeting  in  a  common  point  called 
the  vertex. 

A  right  cone  is  a  solid  resembling  a  pyramid,  but  having  a 
curved  surface,  a  circular  base,  and  its  vertex  always  equally 
distant  from  all  points  in  the  circumference  of  the  base. 

A  pyramid  is  regular  when  besides  being  right,  its  base  is 
a  regular  polygon. 

The  altitude  or  height  of  a  pyramid,  or  of  a  cone,  is  the 
perpendicular  distance  from  the  vertex  to  the  plane  of  the  base. 

The  slant  height  of  a  regular  pyramid  or  cone  is  the  shortest 
distance  from  the  vertex  to  the  boundary  of  the  base. 


278  SPHERES. 

The  frustum  of  a  pyramid  or  cone  is  that  part  that  remains 
after  cutting  off  the  top  by  a  plane  parallel  to  the  base. 

(1.)  To  find  the  entire  surface  of  a  regular  pyramid,  or  of 
a  cone. 

EULE. — Multiply  the  perimeter  or  the  circumference  of  the 
base  by  half  of  the  slant  height,  and  to  the  product  add  the 
area  of  the  base. 

(2.)  To  find  the  solidity  of  any  pyramid  or  cone. 

EULE. — Multiply  the  area  of  the  base  by  one  third  of  the 
altitude. 

(3.)  To  find  the  entire  surface  of  a  frustum  of  a  right  py- 
ramid, or  of  a  cone. 

EULE. — Multiply  the  sum  of  the  perimeters,  or  of  the  cir- 
cumferences of  the  two  ends  by  half  of  the  slant  height,  and  to 
the  product  add  the  areas  of  the  two  ends. 

(4.)  To  find  the  solidity  of  the  frustum  of  any  pyramid, 
or  of  a  cone. 

EULE. — Multiply  the  areas  of  the  two  bases  together,  and 
extract  the  square  root  of  the  product.  This  root  will  be  the 
the  area  of  a  base  which  is  a  mean  between  the  other  two. 
Take  the  sum  of  the  areas  of  the  three  bases,  and  multiply  it 
by  one  third  of  the  altitude;  the  product  will  be  the  solidity. 

E  x  a  m.  pies. 

1.  What  is  the  entire  surface  of  a  right  cone,  the  diameter 
of  the  base,  and  the  slant  height  .being  each  40  feet  ?     What 
its  solidity  ?  Ans.  Entire  surface   3769.92  sq.  ft. 

Solidity  14510.42  cu.  ft. 

2.  What  are  the  contents  of  a  stick  of  round  timber  whose 
length  is  20  feet,  the  diameter  of  the  larger  end  being  12 
inches,  and  of  the  smaller  end  6  inches  ? 

Ans.  9 1  cu.  ft.  nearly. 


SPHERES. 

ART.  181.  A  sphere  is  a  solid  bounded  by  a  curved  surface, 
all  the  points  of  which  are  equally  distant  from  a  point  within 
called  the  center. 


GAUGING.  279 

The  diameter  or  axis  of  a  sphere  is  a  line  passing  through 
the  center,  and  terminated  each  way  by  the  surface. 

The  radius  is  a  line  extending  from  the  center  to  the  sur- 
face, and  is  equal  to  half  the  diameter. 

(1.)  To  find  the  surface  of  a  sphere. 

KULE. — Multiply  the  diameter  by  the  circumference.     Or, 

Multiply  the  square  of  the  diameter  by  fff  or  3.1416. 

(2.)  To  find  the  solidity  of  a  sphere. 

KULE. — Multiply  the  cube,  of  the  diameter  by  £  ff  or  3.1416, 
and  take,  one,  sixth  of  the  product.  Or, 

Multiply  the  area  of  the  surface  by  one  sixth  of  the  diameter. 

E  3C  a  rn  pies. 

1.  How  many  square  miles  on  the  surface  of  the  earth,  it 
being  7912  miles  in  diameter  ?    Ans.  196663355.7504  sq.  m. 

2.  What  are  the  solid  contents  of  a  globe  whose  diameter 
is  10  inches  ?  Ans.  523.6  cu.  in. 

3.  The  surface  of  a  certain  sphere  is  1648  square  feet ; 
what  is  the  surface  of  another  whose  diameter  is  three  times 
as  great  ?  Ans.  14832  sq.  ft. 

4.  What  is  the  diameter  of  a  sphere  containing  ^  of  the 
solidity  of  another  sphere  7|  feet  in  diameter  ?       Ans.  5  ft. 


GAUGING. 

ART.  182.  Gauging  is  the  art  of  measuring  the  capacity 
of  casks  and  vessels  of  any  form.  In  commerce,  most  of  the 
gauging  is  done  by  the  use  of  technical  rules  and  instruments, 
winch  give  only  an  approximate  result ;  perfect  accuracy  by  a 
long  process  being  less  desirable  than  a  tolerable  approxima- 
tion requiring  but  little  skill  and  labor. 

To  gauge  accurately  use  the  following  general 
RULE. — Having  taken  the  necessary  linear  measurements, 
compute  by  the  rules  under  MENSURATION  heretofore  given,  the 
volume  of  the  inside  of  the  cask  or  vessel  in  cubic  inches. 
Divide  this  by  2150.42/0?*  the  measurement  in  bushels,  by  282 
for  beer  gallons,  by  231  for  wine  gallons. 


280  PARTNERSHIP     SETTLEMENTS. 


PARTNERSHIP    SETTLEMENTS. 

ART.  183.  The  true  basis  of  all  partnership  settlements  is 
the  original  agreement  or  contract  between  the  parties. 

To  avoid  misapprehension  and  difficulty,  such  agreements 
should  be  explicit  and  comprehensive  on  all  essential  points  ; 
for,  although  the  legal  construction  of  such  instruments  aims 
at  the  "  intent  of  the  contracting  parties/'  it  is  best  to  save 
the  necessity  of  such  construction,  by  putting  the  intent  in  the 
plainest  possible  English. 

The  following  points  should  be  embraced  in  a  partnership 
contract : 

1.  The  amount,  time  of  investment,  and  continuation  of 
each  partner's  capital. 

2.  The  proportionate  amount  to  be  drawn  by  each  partner 
for  his  private  use. 

3.  The  basis  of  gain  or  loss,  and  each  partner's  proportion 
thereof. 

4.  The  limitation  of  copartnership. 

Other  points  may  be  added,  according  to  the  necessities  of 
the  case  ;  but  great  care  is  necessary  to  avoid  defeating  the 
purposes  of  the  contract  by  verbosity  and  ambiguity  of  terms. 
The  object  of  a  partnership  settlement  is  to  ascertain  the 
relations  in  which  the  partners  stand  to  the  business  and  each 
other.  Such  settlements  should  be  effected  at  least  as  often  as 
once  every  year. 

The  dissolution  of  a  copartnership  may  be  effected  by  the 
expiration  of  the  terms  of  copartnership — the  decease  of  one 
of  the  partners — the  breaking  out  of  a  war  between  the  two 
countries  of  which  the  partners  are  citizens — or  the  mutual 
consent  of  the  partners  themselves. 

After  a  partnership  has  been  dissolved,  and  proper  notice 
given,  one  member  of  the  firm  can  not  bind  the  others  by 
drawing  or  accepting  drafts,  or  by  making  promissory  notes, 


PARTNERSHIP     SETTLEMENTS.  281 

even  for  previously  existing  debts  of  the  firm  ;  and  although 
the  partner  drawing  the  same  was  authorized  to  settle  the 
partnership  affairs. 

If  a  partnership  be  formed  for  a  single  purpose  or  trans- 
action, it  ceases  as  soon  as  the  business  is  completed,  and 
a  settlement  should  be  immediately  effected  between  the 
partners. 

Either  partner  may  dissolve  the  partnership  at  any  time, 
by  giving  notice  to  his  copartners  ;  even  though  it  was  under- 
stood and  agreed  at  commencing,  that  the  partnership  should 
continue  for  a  longer  and  definite  period.  But  the  partner 
thus  dissolving  his  connection  with  the  firm,  will  subject  him- 
self to  a  claim  of  damages  for  breach  of  contract. 

When  notice  of  dissolution  is  given,  and  also  of  the  ap- 
pointment of  one  of  the  partners  to  settle  up  the  business,  a 
settlement  made  by  a  debtor  of  the  firm  with  one  of  the  other 
partners,  without  the  knowledge  and  consent  of  the  partner 
so  appointed,  would  be  fraudulent  and  void. 

The  almost  endless  variety  of  conditions  which  affect  part- 
nership settlement,  renders  it  extremely  difficult  to  give  general 
rules  and  illustrations,  which  will  cover  all  cases.  The  follow- 
ing examples,  however,  will  be  found  both  practical  and  im- 
portant. 

C  A.  S  E     I. 

ART.  134.  The  investment  and  the  resources  and  liabilities 
at  closing,  being  given  to  find  the  net  gain  or  loss. 


Subtract  the  sum  of  the  liabilities  (including  the  invest- 
ment) from  the  sum  of  the  resources  ,  and  the  difference  will 
be  the  net  gain;  or  (if  the  liabilities  are  the  larger)  subtract 
the  sum  of  the  resources  from  the  sum  of  the  liabilities,  and 
the  difference  will  be  the  net  loss. 

Ex.  1.  A  and  B  are  partners.  At  the  close  of  one  year's 
business,  an  inventory  is  taken  showing  the  condition  of  affairs 
to  be  as  follows,  viz.  :  Cash  on  hand  $3278.  Merchandise  in 
store  valued  at  §1500.  Five  shares  City  Bank  Stock  $500. 


282        PARTNERSHIP  SETTLEMENTS. 

House  and  lot  valued  at  §4000.  The  firm  owe  on  their  notes 
$2000,  and  to  Wm.  Brown  on  account,  $1200.  A  invested 
$2426,  B  invested  $2872.  What  is  the  net  gain  ?  Am.  $780. 

Operation. 

Resources.  Liabilities. 

Cash  $3278  Firms'  Notes  $2000 

Merchandise  1500  Due  Wm.  Brown       1200 

City  Bank  Stock     500  A  invested  2426 

House  and  Lot       4000  B       do.  2872 

9278  p498 

_8498 

Net  Gain     $780 

Ex.  2.  C,  D,  and  E  are  partners.  After  conducting  busi- 
ness one  year  they  have  the  following  resources  and  liabilities  : 
Cash  on  hand  f4S60.  Mill  and  fixtures  valued  at  $6924. 
Bills  Keceivable  $896.  Brown  &  Co.  owe  $2000.  Ten  shares 
E.  K.  Stock  $1000.  The  firm  owe  on  notes  outstanding  $6400. 
C  invested  $4500.  D  invested  $3800.  E  invested  $3600. 
What  is  the  net  loss  ?  Ans.  $2620. 

C  .A.  S  IE      II. 

ART.  185.  The  investment,  the  resources  and  liabilities  at 
closing,  and  the  proportion  in  which  the  partners  share  the 
gains  or  losses  being  given  to  find  each  partner's  interest  in 
the  concern  at  closin. 


Find  the  net  gain  or  net  loss  by  Rule  under  Case  I.  Then, 
if  there  is  a  gain,  add  each  partner's  share  of  gain  to  his  in- 
vestment and  subtract  the  amount  he  owes  the  firm.  Or,  if 
there  is  a  loss,  find  each  partner's  share  of  loss  and  subtract 
it  from  his  investment;  also  subtract  any  amount  that  the  part- 
ner oives  the  firm,  as  before. 

Ex.  1.  A  and  B  are  partners.  A  is  to  share  f  of  the  gain 
or  loss,  and  B  f  .  At  the  close  of  business  the  following  is 
shown  to  be  the  condition  of  their  affairs,  viz.  :  Cash  on  hand 
$2680.  Bills  Keceivable  on  hand  $3620.  Five  shares  United 
States  Stock  valued  at  $520.  House  and  lot  valued  at  $6000. 


PARTNERSHIP*     SETTLEMENTS. 


283 


Sturgis  &  Co.  owe  on  account  §1800.  The  firm  owe  on  notes 
outstanding  §2840.  They  owe  G.  P.  Carey  on  account  §890. 
A  invested  §4610.  B  invested  §4860. 

What  is  A's  interest  in  the  concern  ?        Ans.  A  $5178. 
"      "  B's         "         "  "  B  §5712. 


Operation. 


Resources. 
Cash  on  hand 
Bills  Receivable 
U.  S.  Stock 
House  and  Lot 
Sturgis  &  Co.  owe 


Liabilities. 


§2680 
3620 
520 
6000 
1800 
14620 
13200 


Notes  unpaid  §2840 

Due  G.  P.  Carey  890 

A  invested  4610 

B       do.  4860 


Net  Gain      §1420 


5)1420 
*     284        i  " 
3 

§852  B's  |  " 
§568  A's  f  " 


§13200 
Net  Gain, 


Proof. 


£ash  §2680 

Bills  Receivable  3620 

U.  S.  Stock  520 

House  and  Lot  6000 

Sturgis  &  Co.  1800 


Total  Resources  §14620 


Bills  Payable 

G.  P.  Carey 

A  invested        4610 

"  f  Net  Gain    568 

"  present  interest  in  concern 

B  invested        4860 

"     Net  Gain    852 


§2840 
890 


5178 


5712 


"  present  interest  in  concern 
Total  Liabilities  "§14620 


Note. — In  the  following  examples  the  resources  are  sup- 
posed to  be  brought  in  at  their  actual  cash  value.  No  interest 
is  allowed  on  the  partners'  accounts  unless  so  specified. 

Ex.  2.  C,  D,  and  E  are  partners.  To  share  the  gains  or 
losses  each  one  third.  The  resources  and  liabilities  at  the  close 
of  the  year  are  found  to  be  as  follows,  viz. :  Money  deposited 
in  City  Bank  §8460.  Copper  Mine  Stock  valued  at  §10240. 


284  PARTNERSHIP      SETTLEMENTS. 

Bills  Receivable  on  hand  $6420.  Fulton  Bank  Stock  on  hand 
valued  at  $3826.  Block  of  buildings  and  Lot  valued  at 
$35000.  Hall  &  Co.  owe  on  account  $1344.  L.  M.  Howard 
owes  on  account  $960.  The  firm  owe  on  their  notes  unre- 
deemed $5680.  To  Mason  &  Austin  on  account  $1700.  C 
invested  $18420.  D  invested  $18460.  E  invested  $18432. 
What  is  each  partner's  present  interest  in  the  concern  ? 

Ans.  C  $19606,  D  $19646,  E  $19618. 

Ex.  3.  F,  G,  H,  and  I  are  partners.  They  share  the  gains 
or  losses  as  follows,  viz.  :  F  and  G  ^  each,  H  T42-  and  I  T\. 
At  the  close  of  business  the  resources  are  Cash  $4628,  Mer- 
chandise $12620,  Real  Estate  $5000,  Bank  Stock  $3000, 
Wheat  and  Corn  $2800,  Horses  and  Harness  $500,  Lumber 
$520,  Money  deposited  in  Globe  Bank  $8620.  F  has  drawn 
from  the  business  $450,  H  has  drawn  $180.  The  liabilities  of 
the  concern  are,  Notes  unredeemed  $4600,  Due  Simon  Good 
on  account  $800,  Due  S.  S.  Packard  on  account  $1200.  F  in- 
vested $6682.  G  invested  $6682.  H  invested  $8908.  I  in- 
vested $4454.  What  is  each  partner's  interest  in  the  concern? 
Ans.  F  $7480,  G  $7930,  H  $10392,  I  $5286. 

Ex.  4.  J,  K,  L,  M,  and  N  are  partners.  The  gain  or  loss  is 
to  be  divided  as  follows  :  J  T53,  K  T4Tj  L  T\,  M  T2^,  N  JJ} 
Upon  examination  the  following  is  found  to  be  the  condition 
of  affairs  at  the  close  of  business,  viz.  :  Notes  on  hand  against 
other  persons  $12680,  Ohio  State  Stocks  $8420,  New  York 
State  Stock  $6000,  City  Bank  Stock  $2800,  Bonds  and  Mort- 
gages $9460,  Deposit  in  Ocean  Bank  $6742,  Attica  Bank 
owes  the  firm  $4286,  Brown  &  Bros,  owe  $1520,  Interest  on 
Notes,  and  Bonds  and  Mortgages  in  the  hands  of  the  firm 
$688.  Office  Furniture  on  hand  valued  at  $824.  The  liabili- 
ties of  the  concern  are  as  follows,  viz.  :  Notes  and  Acceptances 
outstanding  $5486,  Interest  due  on  firm's  Notes  and  Accept- 
ances $280,  Bal.  favor  Trader's  Bank  $2626,  Bal.  favor  of 
Fulton  Bank  $1500,  N  invested  $2287,  M  invested  $4575, 
K  invested  $9150,  L  invested  $6861,  J  invested  $11455. 
What  has  been  the  Net  Gain  ?  What  is  J's  interest  in  the 
concern?  K's  ?  L's  ?  M's?  N's  ? 


PARTNERSHIP     SETTLEMENTS.  285 

A,is.  Net  Gain  $10200.  J's  interest  $14855.  K's  interest 
$11870.  L's  interest  $8901.  M's  interest  85935.  N's  in- 
terest $2967.  • 

Ex.  5.  There  are  four  partners  in  a  concern,  0,  P,  Q,  and 
K.  Each  partner  to  share  |  of  the  gains  or  losses.  At  disso- 
lution there  is  Cash  on  hand  $6820,  Bills  Keceivable  $8922, 
Croton  Water  Stock  $4500,  Deposit  in  Bank  Commerce 
$3860.  0  has  drawn  from  the  concern  $860,  P  has  drawn 
$575,  Q  has  drawn  $630,  K  has  drawn  $452.  The  liabilities 
are  :  Notes  and  Acceptances  outstanding  $3680,  Bal.  in  favor 
of  Smith  &  Co.  $1264,  in  favor  of  Hall  &  Keed  $860,  Geo. 
Carey  §575.  0  invested  $5590,  P  invested  $5322,  Q  invested 
$5540,  R  invested  $5228.  What  has  been  the  net  gain  or 
loss  ?  What  is  each  partner's  interest  in  the  business  ? 

Ans.  Net  Loss  $1440.  O's  interest  $4370.  P's  $4387. 
Q's  $4550.  R's  $4416. 

C  A.  S  EJ      III. 

ART.  186.  The  resources,  the  liabilities  (except  the  invest- 
ment), and  the  net  gain  or  loss  being  given,  to  find  the  net 
capital  at  commencing. 

RULE. 

When  the  resources  are  larger  than  the  liabilities,  deduct 
the  given  liabilities  from  the  given  resources  (the  difference 
will  be  the  present  worth  of  firm),  and  from  this  remainder 
deduct  the  net  gain,  or  add  the  net  loss.  Or, 

When  the  liabilities  are  greater  than  the  resources,  deduct 
the  resources  from  the  liabilities  (the  difference  will  be  the 
net  insolvency  of  firm),  and  deduct  this  remainder  from  the 
net  loss. 

Note  1. — The  liabilities  can  never  exceed  the  resources  at 
closing  when  there  is  a  capital  at  commencing  and  a  net  gain 
during  business, 

Note  2. — In  the  following  examples  it  is  supposed  that  the 
whole  investment  is  made  at  the  time  of  commencing  business, 
and  that  it  remains  undisturbed  until  the  date  of  partnership 
settlement. 


286 


PARTNERSHIP  SETTLEMENTS. 


Ex.  1.  A  and  B  are  partners.  A  invested  f  and  B  |-  of 
the  capital.  They  are  to  share  equally  in  gains  or  losses.  At 
the  close  of  business  the  resources  are  :  Cash  $6800,  Bills 
Keceivable  $4700,  Merchandise  $6400,  Real  Estate  $5000, 
Bank  Stock  $900,  Steamboat  Stock  $9000.  A  has  drawn 
from  the  business  $365,  B  has  drawn  $526.  The  liabilities 
are  :  Firm's  Notes  unredeemed  $4680,  Bal.  favor  of  S.  S. 
Packard  $620,  J.  T.  Calkins  $476,  R.  H.  Hoadley  $326.  The 
net  gain  during  business  has  been  $2644.  What  was  the  firm 
worth  at  commencing  ?  What  was  each  partner  worth  ? 

Ana.  Firm  $24945.    A  §9978.     B.  $14967. 


Cash 

Bills  Receiv. 
Merchandise 
Real  Estate 


$6800 
4700 
6400 
5000 


Bank  Stock          900 
Steam  Bt.  Stock  9000 

A  is  charged         365 
B        "  526 


$33691 


Cash 

Bills  Receiv. 
Merchandise 
Real  Estate 
Bank  Stock 


$6800 

4700 

6400 

5000 

900 


Steam  Bt.  Stock  9000 


A  is  charged 
B 


365 
526 


$33691 


Operation. 

Bills  Payable 
S.  S.  Packard 
J.  T.  Calkins 
R.  H.  Hoadley 

33691  Resources 

6102  Liabilities 
27589  Present  worth  of  firm 

2644  Net  Gain 


84680 
620 
476 
326 

$6102 


5)24945  Net  Cap.  at  com. 

4989 

2 

9978  A's  |  of  the  Cap.  at  com. 
14967  B's  f 


Proof. 

Bills  Payable 

S.  S.  Packard 

J.  T.  Calkins 

R.  H.  Hoadley 

A's  Cap.  at  com.  9978 
"  i  Net  Gain  1322 
"  Present  worth 

B's  Cap.  at  com.  14967 
"  J  Net  Gain  1322 
"  Present  worth 


?46SO 
620 
476 
326 


11300 

_16289 
$33691 


PARTNERSHIP     SETTLEMENTS.  287 

Ex.  2.  C,  D,  and  E  are  partners.  C  invested  {,  D  f ,  and 
E  |,  to  share  the  gain  or  losses  equally.  At  the  close  of  busi- 
ness the  resources  are  found  to  be  :  Wheat  on  hand  valued  at 
§2600,  Corn  on  hand  $3200,  Flour  $1600,  Mill  and  Fixtures 
$8000.  The  firm  owe  Digby  V.  Bell  $2600,  to  J.  H.  Gold- 
smith $1500,  and  on  their  Notes  unredeemed  §949.  The  net 
loss  in  the  business  has  been  $633.  What  was  the  net  capital 
of  the  firm  at  commencing  ?  What  was  each  partner's  net 
capital  ? 

Ans.  Firm  §10984.  C  $1373.  D  §4119.  E  §5492. 
Ex.  3.  There  are  four  partners  engaged  in  business  as  a  firm, 
F,  G,  H,  and  I.  They  have  been  unfortunate,  the  net  loss 
being  $15320.  On  examination  the  resources  are  found  to  be 
as  follows,  viz.  :  Live  Cattle  on  hand  valued  at  $9680,  Packed 
Beef  valued  at  $12600,  Empty  Barrels  on  hand  valued  at 
$500,  Deposit  in  Drov.ers'  Bank  $2500.  The  firm  owe  on 
their  Notes  and  Acceptances  §22600,  Warren  P.  Spencer  on 
account  $4000,  J.  C.  Bryant  on  account  §6000.  The  partners 
invested  in  equal  amounts  and  are  to  share  the  gains  or  losses 
in  the  same  proportion.  What  was  the  investment  of  the 
firm  ?  What  was  each  partner's  investment  ? 

Ans.  Firm  $8000.  F  §2000.  G  §2000.  H.  §2000.  I  $2000. 

CA.SE      IAT. 

ART.  187.  -When  the  firm  commence  insolvent. 
The  resources  and  liabilities  at  closing,  and  the  net  gain  or 
loss  being  given,  to  find  the  net  insolvency  at  commencing. 

R.  TJH.  IE. 

Wlien  the  liabilities  are  greater  than  the  resources  at 
closing ,  deduct  the  given  resources  from  the  given  liabilities, 
and  to  this  remainder  add  the  net  gain  or  from  it  subtract  the 
net  loss.  Or, 

When  the  resources  are  larger  than  the  liabilities  at 
closing,  deduct  the  liabilities  from  the  resources,  and  deduct 
this  remainder  from  the  net  gain. 

Ex.  1.  A  and  B  are  partners.  They  commence  business 
insolvent.  The  proportion  of  their  insolvency  is  A  |,  B  j. 


288  PARTNERSHIP     SETTLEMENTS. 

The  gains  or  losses  are  to  be  equally  divided.  At  the  close  of 
business  the  resources  are,  Cash  on  hand  $3246,  Lumber  on 
hand  valued  at  $6428,  Timber  and  Logs  valued  at  $3272, 
Bills  Receivable  $1800.  The  firm  owe  on  their  Notes  and 
Acceptances  $9400,  to  E.  R.  Felton  on  account  $3684,  to  H. 
W.  Ellsworth  on  account  $2160.  The  net  gain  during  busi- 
ness has  been  $1568.  What  was  the  net  insolvency  of  the 
firm  at  commencing  ?  What  was  each  partner's  net  insolvency 
at  commencing  ? 

Ans.  Finn's  $2066.     A's  $1549.50.     B's  $516  50. 

Operation. 

Cash  on  hand                 $3246  Bills  Payable               $9400 

Lumber     "                       6428  E.  R.  Felton                  3684 

Timber  and  Logs  on  h.     3272  H.  W.  Ellsworth           2160 

Bills  Receivable       "        1800  

$"14746  $15244 

$15244  Liabilities 

4)2066  Net  Insolv.  at  com.  14746  Resources 

516.50  B's  i     "       «  ~^98~Pres.  Net  Insolv.  of  firm 

3_  1568  Net  Gain 

$1549.50  A's  |    "       "  2066  Insolv.  of  firm  at  com. 

Proof. 

Cash  $3246       Bills  Payable  $9400.00 

Lumber  6428      E.  R.  Felton  3684.00 

Timber  and  Logs  3272      H.  W.  Ellsworth        2160.00 

Bills  Receivable  1800      B's  £  Net  Gain  784.00 

A's  Insolv.  at  com.  1549.50  "  Ins,  at  com.  516.50 

"  J  Net  Gain       784  "  Net  Capital  ~  ~26750.00 

"  Net  Insolvency    .     .     765.50 
Tot.  Resources  of  firm  $1551150    Tot.  Liab.  of  firm"|l5511~50 

Eemarlc. — In  the  foregoing  example  the  partners  were  both 
insolvent  at  commencing  business.  The  business  was  profit- 
able, and  B's  share  of  the  gain  was  more  than  his  insolvency 
at  commencing,  so  that  he  ends  with  a  net  capital.  A  is  still 
insolvent,  but  to  a  less  amount  than  when  he  commenced. 


PARTNERSHIP    SETTLEMENTS.  289 

Ex.  2.  C,  D,  E,  and  F  are  partners,  commencing  with 
equal  insolvency,  the  gains  or  losses  to  be  shared  as  follows, 
viz. :  C  T3o,  D  T42?  E  T22>  &  T32'  Two  years  having  passed  an 
inventory  is  taken,  showing  the  following  condition  of  affairs  : 
20000  Ibs.  Cheese  on  hand  @  8  cents,  $1600  ;  40000  Ibs.  But- 
ter @  18  cents,  $7200  ;  2000  bush.  Potatoes  @  40  cents,  $800  ; 
3000  bush.  Wheat  @  90  cents,  $2700.  The  firm  owe  on  their 
Notes  and  Acceptances  $8628.  They  owe  E.  B.  Kockwell 
on  account  $3242.  They  owe  W.  H.  Clark  on  account  $4563. 
There  has  been  a  net  loss  during  the  business  of  $528.  What 
was  the  net  insolvency  of  the  firm  at  commencing  ?  What 
was  the  net  insolvency  of  each  partner  ?  What  is  the  net  in- 
solvency of  each  partner  at  closing  ? 

Ans.  Insolvency  of  firm  at  com.  $3605.     Insolvency  of  each 

partner  $901.25.    Insolvency  of  firm  at  closing  $4133. 

C  $769.25.     D  $725.25.     E  $813.25.     F  $769.25. 

Ex.  3.  G,  H,  I,  J,  and  K  formed  themselves  into  a  co- 
partnership for  the  purpose  of  carrying  on  the  building  and 
masonry  business.  The  firm  to  assume  the  liabilities  of  the 
partners.  The  proportion  in  which  the  partners  are  insolvent 
at  commencing  is  as  follows,  viz.  :  Gr  -f-g,  H  ^  I  ^  J  ^ 
and  K  ^V  The  gains  or  losses  are  to  be  divided  in  the  pro- 
portion of  their  insolvency.  At  the  close  of  business  the  fol- 
lowing is  the  condition  of  affairs :  Deposit  in  City  Bank 
$5428,  Bonds  and  Mortgages  Kec.  $3826,  Notes  and  Drafts 
$6294.  J.  C.  Bryant  owes  on  account  $4466,  Brick  and 
Stone  on  hand  valued  at  $3688.  The  firm  owe  on  their  Notes 
and  Acceptances  $18000.  They  owe  Baldwin  &  Co.  $3620. 
The  Net  Gain  has  been  $5622.  What  was  the  net  insolvency 
of  firm  at  commencing  ?  What  was  the  insolvency  of  each 
partner  ?  What  is  the  net  capital  of  firm  at  closing  ?  Of 
each  partner  ? 

Ans.  Insolvency  of  firm  at  commencing  $3540.  Of 
G  $354,  H  $531,  I  $708,  J  $885,  K  $1062. 
Net  capital  of  firm  at  closing 
H$ ,I8^ 

19 


290  PARTNERSHIP      SETTLEMENTS. 


MISCELLANEOUS. 

1.  D.  Y.  Bell,  J.  H.  Goldsmith,  E.  G-.  Folsom,  and  J.  C. 
Bryant,  are  partners.    The  two  former  furnish  the  capital,  and 
the  two  latter  are  to  bear  the  expenses  of  conducting  the  busi- 
ness, each  one  half.     The  profits  or  losses  are  to  be  distributed 
as  follows  :  Bell  ^  Goldsmith  Yflu?  Folsom  ^,  and  Bryant  ^. 
Bell  advanced  at  commencing  business  $18423.     Goldsmith 
advanced  $13142.     At  the  close  of  the  year  it  is  ascertained 
that  the  profits  have  exceeded  the  losses  (not  including  ex- 
penses)  $6823.80.      The   expense   account   has  an   excess  of 
debits  of  $2412.08.    Bell  has  drawn  out  during  business  $426. 
Folsom  has  drawn  but  $2342.13.     What  is  each  partner's  in- 
terest in  the  concern  at  the  close  of  the  year  ? 

Note. — In  the  above  example  Mr.  Goldsmith  was  allowed 
to  draw  a  large  amount  from  the  business,  and  by  consent  of 
the  other  partners  was  not  to  pay  interest  upon  it.  Interest 
is  not  to  be  taken  into  account  in  solving  this  and  the  follow- 
ing examples  unless  it  is  so  specified. 

2.  S.  S.  Packard,  J.  T.  Calkins,  and  E.  B.  Rockwell  are 
partners,  to  share  the  gains  or  losses  equally.     At  the  close  of 
one  year  the  following  is  the  result  of  the  business  :  Cash  on 
hand  $8920,  Bills  Receiv.  $6273,  Merchandise  $5682,  Bank      ]/ 
Stock  $896,  Mr.  Packard  has  drawn  from  the  concern  $672.43, 

Mr.  Calkins  $2471.04,  Mr.  Rockwell  $1896.06.  Bills  Payable 
outstanding  §5957.95.  Packard  invested  $7420,  Calkins  in- 
vested $6812,  Rockwell  invested  $4635.  What  has  been  the 
gain  or  loss  ?  What  is  each  partner's  present  interest  in  the 
concern  ? 

3.  R.  W.  Hoadley,  H.  W.  Ellsworth,  and  H.  C.  Spencer 
are  partners.     They  invest  in  equal  amounts,  and  share  gains 
and  losses  equally.     At  the  expiration  of  two  years  they"  have 
Cash  on  hand  $7242,  R.  R.  Stock  $4860,  Real  Estate  $4673, 
Produce    $2921.       They    have    Bills     Payable    outstanding 
$2326.41.      During  business   Mr.  Ellsworth   has   withdrawn 
from  the  concern  $924,  and  Mr.  Spencer  has  advanced  to  the 


PARTNERSHIP     SETTLEMENTS.  291 

concern  $1138.  The  total  losses  have  been  $754.25,  the  total 
gains  §3269.54.  What  is  each  partner's  share  of  gain  or  loss  ? 
What  was  each  worth  at  commencing  ?  What  is  each  part- 
ner's" interest  in  the  concern  at  closing  ? 

4.  R.  C.  Spencer,  W.  H.   Clark,  L.  Fairbanks,  and  C.  E. 
Wilber  have  been  associated  in  business  during  the  past  three 
years.     The  books  have  remained  unclosed  to  this  date. 

R.  C.  S.  invested  at  commencement  of  business  $6824.00 

W.  H.  C.  "  "  "  5982.00 

L.  F.  "  "  "  7126.00 

C.  E.  W.  "  "  "  4998.00. 

They  are  to  share  equally  in  gains  or  losses.     Since  the  books 

were  opened  the  partners  have  made  the  following  additional 

investments  :  R.  C.  S.  $2128.40,  W.  H.   C.  $684.12,  L.  F. 

81242.78,  C.  E.  W.  §946.64.     The  partners  have  each  drawn 

from  the  concern  the  following  amounts  :  R.  C.  S.  $8126.42, 

W.  H.  C.  $5274.18,  L.  F.  §8232.64,    C.  E.  W.  $3178.26. 

There  are  no  resources  or  liabilities  at  this  date  except  such  as 

are  shown  by  the  partners'  accounts.     Has  the  business  been 

prosperous  or  adverse  ?     If  a  dissolution  now  take  place,  how 

shall  the  partners  settle  with  each  other  ? 

5.  G.  B.  Collins,  A.  H.  Redington,  and  Alonzo  Gaston 
were  partners  in  a  manufacturing  business,  commencing  July 
1st,  1856.   At  that  date  G.  B.  C.  put  into  the  concern  $1600, 
A.  H.  R.  put  in  §4000,  A.  G.  made  no  investment,  but  was  to 
superintend  the  business.    They  were  to  share  equally  in  gains 
or  losses.     Six  per  cent,  interest  to  be  allowed  on  each  side  of 
the  partners'  accounts.  The  books  are  not  closed  until  July  1st, 
1858,  when  the  following  statement  is  rendered  by  the  book- 
keeper :    G.  B.  C.  has  drawn  from  the  concern  at  different 
times  to  the  amount  of  $14760,  the  average  date  at  which  it 
was  drawn,  being  September  12th,  1857.     A.  H.  R.  has  drawn 
$11380,  average  date  January  22d,  1858.     A.  G.  has  drawn 
§16240,  average  date  May  16th,  1857.    G.  B.  C.'s  total  invest- 
ment has  been  $2982,  average  date  August  17th,  1857.  A.  H. 
R/s  total  investment  $6824,  average  date  October  9th,  1856. 
A.  G.'s  total  investment  $1528,  average  date  April  24th,  1858. 


292  PARTNERSHIP     SETTLEMENTS. 

Cash  on  hand  $628,  Cash  in  Bank  $2892,  Bills  Keceivable  on 
hand  $5462,  Real  Estate  $7586,  Manufactured  Articles  $4327, 
Personal  Accounts  $1523,  R.  E.  Stocks  $837,  Bills  Payable 
unredeemed  $6248,  Balance  due  on  personal  accounts  $4895. 

What  has  been  the  net  gain  or  loss  of  the  firm  ?  What 
is  each  partner's  present  interest  in  the  concern  ? 

A.  H.  R.  proposes  to  retire  from  the  business,  and  the  other 
partners  agree  to  give  him  $900  more  than  the  books  show  to 
be  due  him.  How  much  will  he  receive  ? 

6.  A  of  New  York,  and  B  of  Ohio,  enter  into  an  arrange- 
ment to  buy  and  sell  Cattle,  and  share  equally  in  gains  and 
losses  ;  B  to  make  the  purchases,  and  A  to  effect  most  of  the 
sales.     A  forwarded  to  B  a  draft  of  $8000,  B  made  purchases 
to  the  amount  of  $13682.24.     B  has  forwarded  cattle  to  A 
during  the  season,  from  which  he  has  made  sales  to  the  amount 
of  $9241.18.     B  has  made  sales  to  the  amount  of  $2836.24. 
A  has  paid  out  for  expenses  $364.16.     B  has  paid  out  for  ex- 
penses $239.14.     At  the  close  of  the  season  B  has  on  hand 
a  number  of  cattle  the  cost  of  which  was  $2327.34.     A  has  a 
quantity  on  hand  which  are  estimated  to  be  worth,  in  the  New 
York  market,  $3123.42.    The  parties  now  propose  to  dissolve 
the  copartnership,  each  taking  the  stock  he  has  in  his  posses- 
sion at  the  figures  given  above,  and  the  balance  in  their  ac- 
counts, if  any,  to  be  paid  in  cash.  What  has  been  the  gain  or 
loss  ?    What  is  each  partner's  share  of  gain  or  loss  ?    What  is 
the  cash  balance  to  be  paid,  and  which  partner  is  to  receive  it  ? 

7.  C  and  D  make  a  contract  with  government  to  do  a  cer- 
tain piece  of  work,  which  is  divided  into  three  sections,  for 
which  they  are  to  receive  as  follows,  provided  the  work  all 
pass  as  No.  1  on  being  inspected  :  for  Section  1,  $1842,  for   y 
Section  2,  $1275,  for  Section  3,  $1563.     If  any  portion  of 
the  work  pass  as  No.  2  on  inspection,  15  per  cent,  will  be  de- 
ducted from  the  original  estimate  ;  if  any  portion  as  No.  3, 
20  per  cent,  will  be  deducted.     The  following  is  the  result  of 
the  inspection  : 

Section  1,  passes  as  No.  1.  Section  2,  as  No.  3,  and  Sec- 
tion 3,  as  No.  2. 


PARTNERSHIP      SETTLEMENTS.  293 

0  has  drawn  from  government  $728.42.  D  has  drawn 
§1226.14.  D  has  made  disbursements  to  the  amount  of 
$1342.25.  C  has  made  disbursements  on  the  work  to  the 
amount  of  §987.45.  What  has  been  the  gain  or  loss  ?  How 
much  is  due  C  ?  How  much  is  due  D  ? 

8.  Two  persons,  E  and  F,  enter  into  business  under  an 
agreement  that  E  shall  draw  from  the  concern  weekly  $5  more 
than  F.    Subsequently  F  lends  E  $260  from  his  private  funds, 
with  the  understanding  that  they  were  then  to  draw  an  equal 
sum   weekly  until   the  loan  be  liquidated.      How  long  will 
it  take  ? 

9.  Three  mechanics  are  partners.     They  agree  that  each 
shall  pay  $2.25  per  day  for  all  working  days  that  he  is  absent 
from  the  business.     At  the  close  of  the  year  it  is  found  that 
A  has  lost  44  days,  B  28  days,  C   12  days.     How  will  the 
partners  adjust  the  matter  between  them  ? 

10.  A,  B,  and  C  enter  into   a  copartnership,  each  in- 
vesting $5000.     A  is  worth  to  the  business  $1500  a  year  ;   B 
$1200 ;  C   §1000.     At  the  end  of  two  months  B  draws  out 
$500,  and  A  adds  to  his  capital  $1000.     At  the  end  of  five 
months,  C  withdraws  §300.     They  close  up  their  business  at 
the  end  of  a  year,  and  find  that  a  net  profit  has  been  realized 
of  $3500.      What  proportion  of  this  gain  belongs   to  each 
partner,  if  money  is  worth  7  per  cent,  per  annum  ? 

11.  Again  :  A,  B,  and  C  are  partners,  each  investing  at 
the  commencement  of  business  $5000,  and  each  being  of  equal 
value  to  the  business.    They  draw  from  and  add  to  the  capital, 
as  before,  and  at  the  end  of  the  year  ascertain  their  gain  to  be, 
as  before,  $3500.     How  will  the  gain  be  equitably  divided  ? 
And  should  the  value  of  money,  as  in  the  former  case,  have 
any  efiect  on  the  adjustment  of  gains  ? 

12.  Again :  A,  B,  and  C  are  partners,  investing  as  in  the 
former  two  instances,  with  the  understanding  that  C  shall  con- 
duct the  business,  for  which  he  is  to  receive  a  commission  of 
25  per  cent,  on  the  net  gain.     The  additions  and  withdrawals 
the  same  as  above,  and  also  the  gain.     How  much  of  the  gain 
should  each  have  ? 


294       PARTNERSHIP  SETTLEMENTS. 

13.  There  are  five  partners  in  a  concern,  sharing  the  gains 
or  losses  equally.     The  liabilities  of  the  firm  have  been  can- 
celed, after  which  the  remaining  effects  were  appropriated  by 
the  partners  without  regard  to  the  proper  proportion   that 
each  should  take.     The  following  is  the  condition  of  the  part- 
ners' accounts,  as  they  now  stand.     A  invested  $5680,  and 
has  drawn  from  the  concern  §4700.     B  invested  $4780,  and 
has  drawn  $4400.     C  invested  $4980,  and  has  drawn  $4600. 
D  invested  $3984,  and  has  drawn  $3300.     E  invested  $5600, 
and  has  drawn  $5346.     How  will  the  partners  settle  with 
each  other  ? 

14.  A  and  B  are  partners.     They  have  Cash  and  Collect- 
able Paper  on  hand  to  the  amount  of  $5280.11.    A  has  drawn 
from  the  concern  $2446.80,  B  has  drawn  $905.98.     A  put 
into  the  concern  $3127.25,  B  put  in  $448.75.     The  firm  owe 
on  Paper  and  Book  Debts  $4005.48.     What  is  each  partner's 
present  interest  in  the  concern,  if  they  share  equally  in  gains 
and  losses  ? 

15.  S.  S.  Guthrie  and  H.  C.  Walker  purchased  a  vessel  on 
joint  account,  for  which  they  paid  $8400,  Mr.  G.  taking  one 
third  interest  and  Mr.  W.  two  thirds. 

During  the  season  G.  paid  for  supplies,  repairs  and 

sundry  expenses $956.00 

And  received  Cash  from  freight  and  passage  receipts  2686.40 

W.  paid  for  repairs,  supplies,  &c.         .        .         .      1548.26 

And  received  Cash  from  freight  and  passage  receipts  4862.48 

At  the  close  of  the  season  they  sell  the  vessel  for  $9000, 

receiving  one  half  in  Cash,  and  the  purchaser's  Note  for  one 

half. 

W.  agrees  to  take  this  Note,  to  apply  on  his  account,  at 
^%  discount,  which  G.  assents  to  ;  and  then  the  $4500  Cash 
is  properly  divided  between  the  two  partners ;  how  much  is 
taken  by  each  ? 

16.  Alonzo  Gaston  and  G.  B.  Collins  take  a  contract  of 
A.  H.  Kedington  to  sink  an  aqueduct  of  a  certain  width  50 
rods  in  length,  and  if  it  average  10  feet  deep,  they  are  to 
receive  for  constructing  the  same  $26  per  rod.   If  on  measure- 


PARTNERSHIP     SETTLEMENTS.  295 

ment  it  average  less  than  10  feet,  3$  will  be  deducted  for  the 
first  6  inches,  6%  for  the  second  6  inches,  9$  for  the  third  6 
inches. 

A.  G.  has  paid  out  for  wages  and  material     $158 
G.  B.  C.  "  "  "  $536 

A.  H.  R.  has  advanced  $488,  of  which  A.  G.  received  $242.18, 
G.  B.  C.  received  $245.82.  The  average  depth  was  to  he  ascer- 
tained by  measurement  at  the  end  of  every  five  rods,  which 
resulted  as  follows  : 

ft.  in.  ft.    in. 

End  of  1st  five  rods  10  4  End  of  6th  five  rods  7  10 

"  2d  "  10  9  "  7th  "  84 

"  3d  «  98  "  8th  "  79 

"  4th  "94  "  9th  "  9  7 

"  5th  "83  "  10th  "  88 

What  has  been  the  gain  or  loss  ?     How  much  is  due  from  A. 

H.  R.  ?     How  will  Mr.  Gaston  and  Mr.  Collins  settle  with 

each  other  ? 

17.  A  and  B  contracted  with  Kussell  &  Co.  to  erect  a 
Steam  Flouring  Mill  for  $11000.    Not  wishing  to  be  burdened 
with  the  salary  of  a  bookkeeper,  it  was  arranged  that  each 
partner  should  keep  a  strict  account  of  all  his  receipts  and  ex- 
penditures, and  report  at  the  completion  of  the  contract,  at 
which  time  they  would  have  a  general  settlement.     On  the 
fulfillment  of  the  contract  they  find  their  affairs  standing  as 
follows,  viz.  :  A  has  paid  out  for  building  material  and  wages 
$2862.48.     He  has  received  from  Russell  &  Co.  at  different 
times  to  the  amount  of  $1324.08.    B  has  paid  out  for  building 
material  and  wages  $4788.04.     He  has  received  from  Eussell 
&  Co.  ?5024.44.     There  is  due  the  hands  for  wages  $410. 

What  has  been  the1  profit  ?  How  much  is  due  from  Russell 
&  Co.  ?  And  how  much  of  it  should  be  paid  to  A  ?  How 
much  to  B  ? 

18.  E.  C.  Bradford,  Joseph  Dawson,  and  E.  Young  have 
been  doing  business  together  as  partners,  with  the  understand- 
ing that  Mr.  B.  should  receive  a  salary  of  $1200,  for  managing 
the  concern,  the  other  partners'  time  not  to  be  required  in  the 
business.     Interest  to  be  allowed  on  both  sides  of  each  part- 


296  PARTNERSHIP     SETTLEMENTS. 

ner's  account.  The  profits  or  losses  to  be  divided  equally  be- 
tween them.  Mr.  B.  invested  January  1,  I860,  $6000,  May  2, 
$350,  October  12,  $500.  He  drew  out  February  8,  $250, 
April  4,  $380,  July  5,  $620,  November  20,  $782.  Mr.  D. 
invested  January  1,  $5400,  June  12,  860,  $280,  October  3, 
$365,  December  18,  $428.  He  drew  out  March  2,  $468,  May 
21,  $428,  August  3,  $542,  September  15,  $247,  December  19, 
$388.  Mr.  Y.  invested  January  1,  $4896,  May  9,  $356,  July  2, 
$428.  He  drew  out  March  13,  $355,  June  3,  $126,  August  9, 
$281,  October  6,  $126,  December  24,  $43£.  On  December  31, 
I860,  one  year  from  the  day  of  commencing  business,  the  re- 
sources and  liabilities  (not  including  the  partners'  accounts) 
are  as  follows,  viz. : 

Cash  on  hand  ....  $5680 
Bills  Keceivable  on  hand  .  .  .  4366 
Heal  Estate  "...  5200 

Bank  Stock  "  ...      5388 

$20634 

Bills  Payable  unredeemed        .         .       $1298.40 
What  is  the  net  capital  of  the  firm  at  closing  ?     What  is 
each  partner's  interest  in  the  concern  at  closing  ? 

19.  The  following  "  Statement/'  taken  from  a  single  entry 
ledger,  in  part,  the  balance  being  made  up  from  inventories 
and  estimates  shows  the  present  condition  of  the  affairs  of  the 
firm  of  A  &  B. 

RESOURCES  TAKEN  FROM  THE  LEDGER. 

John  Smith  owes $460.00 

Wm.  Brown     " 680.00 

Geo.  Carey       " 1260.00 

Wm.  Dudley    " 870.00 

Geo.  Bryant     " 260.00 

Amos  Dean      " 890.00 

A  has  drawn  from  the  concern    !  2400.00 

B         "  "  " 1261.00 

LIABILITIES  TAKEN   FROM   THE   LEDGER. 

Due  Baldwin  &  Co.,  on  account       ....     $546.00 

A  invested 11600.00 

B         "  .  13742.00 


PARTNERSHIP     SETTLEMENTS.  297 

RESOURCES  NOT   SHOWN   ON   LEDGER,    TAKEN   FROM 
INVENTORIES   AND   ESTIMATES. 

Merchandise  on  hand,  per  Inv.            .         .         .  $9685.00 

Notes  and  Drafts  on  hand,  per  B.  B.  (Face)  .         .  5672.00 

Store  Fixtures  on  hand 384.00 

Horses,  Carriages,  and  Harnesses      ....  865.00 

Stable  and  Feed 1262.00 

City  Bank  Stock 892.00 

House  and  Lot  valued  at 6000.00 

C.  C.  &  C.  R.  R.  Stock  valued  at     ....  1820.00 

Bent  paid  in  advance 600.00 

LIABILITIES   NOT    SHOWN    ON   LEDGER. 

Firm's  Notes  and  Acceptances  outstanding  (Face)  $3826.00 
Mortgage  on  House  and  Lot 500.00 

ADDITIONAL   ITEMS   OF    RESOURCE   AND    LIABILITY. 

The  interest  upon  the  Notes  and  Drafts  that  are  on 

hand,  computed  up  to  this  date,  is        ...     $694.00 
The  interest  upon  the  Notes  and  Drafts  that  the  firm 

owe,  computed  to  this  date,  is  ...  148.00 

A  was  to  share  f  of  the  gain  or  loss,  and  B  f .  What  was 
the  firm  worth  at  commencing  business  ?  What  is  the  firm 
worth  at  the  close  of  business  ?  What  has  been  the  net  gain 
or  net  loss  of  firm  ?  What  is  each  partner's  interest  in  the 
concern  at  closing  ? 

20.  Wrn.  H.  Kinne  and  Edward  Rice  are  partners  in  the 
Stone  business.  They  have  a  Stone  Yard,  and  buy  and  sell 
that  material.  Their  books  are  kept  by  single  entry.  The 
books  run  four  years  before  they  are  closed.  An  Inventory  is 
taken  and  a  Statement  made  up  at  the  close  of  the  first  year. 
At  the  close  of  the  second  year,  the  party  having  charge  of 
the  books  neglects  to  do  this.  At  the  close  of  the  third  year, 
the  Inventory  and  Statement  are  made  up,  showing  the  result 
of  two  years'  business.  The  Statement  and  Inventory  are 
made  up  again  at  the  close  of  the  fourth  year. 

The  profits  or  losses  of  the  first  year  are  to  be  divided  as 
follows,  viz. :  Wm.  H.  Kinne  |,  Edward  Rice  £. 


298 


PARTNERSHIP    SETTLEMENTS. 


At  the  commencement  of  the  second  year  J.  G.  Kanney  is 
admitted  as  a  partner,  the  three  partners  to  be  equally  in- 
terested in  gains  or  losses. 

The  following  Statements  were  made  out  at  the  close  of 
the  first,  third,  and  fourth  years. 


1856  to  1857.     1st  year's  business. 


Cash  on  hand 

W.  H.  Kinne — paid  him     . 
Stone  on  hand 
Balances  on  Ledger     . 
Edward  Eice — advanced  by  him 
Gains 


Resources. 

$1260.11 

786.49 

430.66 

6945.00 


$9422.26 


Liabilities. 


$2675.44 

6746.82 

$9422^6 


1857—1858  to  1859.     2d  and  3d  years'  business. 


Edward  Kice — paid  him          .         $2675.44 

"         advanced  last  year 
"        "        paid  him       .        .       829.58 
W.  H.  Kinne       "      "  .         2947.73 

J.  G.  Kanney       "       "  1535.39 

Balances  on  Ledger  .         .         7039.67 

"          "         "       last  year 

Gains       ...... 

$15027.81 

1859  to  1860.     4th  years'  business. 


$2675.44 


6945.00 
.  5407.37 
$15027.81 


Edward  Kice — paid  him 

Win.  H.  Kinne    "  "      . 

J.  £.  Kanney        "  " 

Balances  on  Ledger  . 

"          "         "  last  year 
Stone  on  hand    . 
Gains 


$1014.47 

1543.16 

.     557.95 

10137.06 

981.49 


$14234.13 


$7039.67 

_  7194.46 
$14234.13 


The  above  Statements  are  given  precisely  as  they  were 
made  up  by  one  of  the  partners  who  handed  them  to  us  for 


P  A  R  T  N  BOl  SHIP  -SETTLEMENTS.  299 

^adjustment.  The  student  will  please  exercise  his  skill  in  pro- 
ducing the  best  form  of  Statement  for  showing  clearly  and 
conclusively  each  of  the  answers  to  the  following  questions. 

How  much  is  the  firm  worth  at  the  close  of  each  year,  and 
what  does  the  property  consist  of  ?  What  is  each  partner's 
nterest  in  the  concern  at  the  close  of  each  year  ? 


SUPPLEMENT. 


RATES  OF  INTEREST  ASTD  STATUTE  LIMITATIONS 
IN  THE   UNITED  STATES. 


STATES. 

1 

! 

Allowed 
by  contract. 

PENALTY  FO2  USURY. 

Statute 
Limitations. 

« 
\ 

1 
£ 

Judgments. 

c 
S 
6 
10 
G 
6 
G 
7 
6 
G 
G 
G 
5 
G 
G 
G 
7 
7 

G 

6 

G 
6 

7 

6 

G 
G 
6 
7 
G 
8 
6 
G 
7 

% 

10 
18 

8 
10 
10 
8 

10 
Free 

10 
10 

10 
12 

12 

Forfeiture  of  entire  interest  

yrs. 
3 
3 
1 
6 
3 
5 
4 
5 
6 

1 
3 
6 
3 
6 
6 

3 
5 
6 
6 

6 
3 
6 
6 
6 
4 
3 
2 
6 
5 
6 

yrs. 
6 
5 
4 
6 
6 
5 
6 
5 
20 
5 
5 
5 
6 
3 
6 
6 
6 
6 
10 
6 
16 

6 
3 
15 
6 
6 
4 
6 
4 
6 
5 
6 

yrs. 
20 
10 
5 
17 

20 
20 
20 
20 

15 

20 
12 

10 
7 
20 
20 
16 

20 

20 
20 

16 

8 
20 

Arkansas 

California  

Forfeiture  of  entire  interest  

Connecticut 

Delaware 

principal  

Florida  
Georffi0 

Forfeiture  entire  interest.  

"        excess  of  interest  

Illinois  

"         entire  interest  

Usurious  interest  recoverable.  .  .  . 

Iowa 

ti                  U            .              (( 

Kentucky  
Louisiana 

"      excess  void.  . 

Forfeiture  of  entire  interest  

Usurious  excess  void. 

Maryland 

Forfeit  of  usur  v  

Massachusetts.  .  . 
Michigan 

Forfeit  3  fold  usurious  interest  taken  
Usurious  excess  void  

Minnesota  

Forfeiture  of  interest  

Mississippi. 

Missouri 

Forfeit  entire  interest  

New  Hampshire.  . 
New  Jersey  
New  York  

Forft.  3  fold  usurious  interest  taken  
Contract  void  

f  Con.  void.     Fine  not  over  $100,  and  im- 
prisonment not  over  6  mos.,  or  both.  .  . 
Forfeit  double  the  debt     .             .    . 

North  Carolina.  .  . 
Ohio 

Usurious  excess  void  

Pennsylvania  .... 
Ehode  Island  .... 
South  Carolina.  .  . 
Tennessee  

Forfeit  entire  principal  and  interest 

Usurious  excess  void  .      . 

Forfeit  entire  interest  

Fine  at  least  $10  

Texas     .  .  . 

Forfeit  entire  interest         •     .  -t              . 

Vermont  

"Virginia              > 

Contract  void               .                              .  . 

Wisconsin  .  . 

Forfeit  entire  debt.. 

*  Corporations  excepted. 


302  SUPPLEMENT. 


EXCHANGE    TABLES. 

[COMPILED  MAINLY  FROM  TATE'S  MODERN  CAMBIST, 
AND  THE  BANKERS'  MAGAZINE.] 


GREAT  BRITAIN. 

MONEY  OF  ACCOUNT. — 1  pound =12  shillings =2 40  pence,  called 
Sterling  money,  to  distinguish  it  from  Colonial  money,  and 
other  moneys  of  the  Continent  having  the  same  denomina- 
tions. 

PAR  OF  EXCHANGE. — 1  sovereign =£1=  $4. 86 1.* 

FRANCE. 

MONEY  OF  ACCOUNT.— 1  franc =100  centimes.  Formerly  livres 
and  sous  were  used;  81  livres=80  frcs.,  and  1  sou=5  centimes. 

PAR  OF  EXCHANGE. — 20  francs  gold=15s.  lO^d.  sterling=$3.84. 
Or,  $1=5  frcs.  21  centimes,  or  £1=25  frcs.  22  centimes. 

AMSTERDAM. 

MONEY  OF  ACCOUNT. — 6  florins  or  guilders =600  centimes =120 
stivers=240  grotes  Flemish=20  schillings  Flemish=2f  rix 
dollars. 

PAR  OF  EXCHANGE. — 12  florins  9  centimes =£1=  $4. 86 f.  Or,  1 
florin =$0.40.  In  the  U.  S.  the  quotations  of  exchange  on 
Amsterdam  are  so  many  cents  per  florin  or  guilder. 

BELGIUM. 

MONEY  OF  ACCOUNT. — The  official  money  of  account  is  kept  in 
francs  and  centimes  the  same  as  in  France.  But  in  mercantile 
accounts  and  exchange  it  is  generally  in  florins  and  centimes, 
as  in  Amsterdam — the  denominations  of  schillings  and  grotes 
being  sometimes  used  in  London  Exchange. 


*  This  value  of  the  pound  sterling  is  TV  of  a  cent  lower  than  that  given  on 
page  164,  as  here  the  weight  of  the  sovereign  is  taken  to  be  123£££  grains  in- 
stead of  123^  grains,  as  assumed  there. 


S  U  P  P  L,E  M  E  N  T  .  303 

PAR  OF  EXCHANGE. — The  fixed  relative  value  of  the  franc  to  the 
florin  is  47|  centimes  of  a  florin =1  franc.  25  frcs.  22  cen- 
times=12  florins  9  centimes=40  schillings  3  grotes=£l  = 


$4.86f. 


HAMBURG. 


MONEY  OP  ACCOUNT. — There  are  two  standards  in  Hamburg,  the 
one  Banco  and  the  other  currency — the  former  being  from  20 
to  26^  higher  than  the  latter,  varying  with  the  market  price 
of  fine  silver.  The  former  is  used  in  wholesale  business  and 
in  exchanges,  and  is  nominal ;  while  the  latter  is  used  in  the 
smaller  trade,  and  is  represented  by  corns  in  circulation.  The 
Cologne  mark  weight,  of  the  Hamburg  standard,  is  3608  grains 
Troy ;  and  this  weight  of  fine  silver  is  assumed  to  be  divided 
into  27f  marks  banco,  but  is  coined  into  34  marks  current. 
The  denominations  in  the  two  valuations  being  the  same,  the 
terms  banco  and  current  are  used  to  distinguish  the  standard. 
1  mark=16  schillings =192  pfennings.  3  marks,  or  48  schil- 
lings, are  called  in  exchange  a  rix  dollar. 

PAR  OF  EXCHANGE. — 13  marks  10|   schil.  banco    =£l=$4.86|. 
16      "        12~       "      cwm?w*=£l=$4.86*. 
Or,  1  mark  banco  =  3 5  ^  cents.     In  the  U.  S.  the  quotations  of 
exchange  on  Hamburg  are  so  many  cents  per  mark  banco. 

PRUSSIA. 

MONEY  OF  ACCOUNT. — 1  Prussian  dollar =30  silver  groschen. 

PAR  OF  EXCHANGE. — 1  Cologne  mark  weight  of  fine  silver  is 
coined  into  14  dollars  ;  hence,  6  Prussian  dollars  27  silver 
groschen  =  £l  =  $4.86f. 

RUSSIA. 

MONEY  OF  ACCOUNT. — 1  ruble =100  copecs.  100  silver  rubles  = 
350  paper  or  bank  rubles — the  latter  being  the  money  of  ac- 
count, previously  to  July,  1839. 

PAR  OF  EXCHANGE. — 1  silver  ruble=37^d.  sterling.  At  Odessa 
the  rate  of  exchange  on  London  is  still  generally  made  in  paper 
rubles,  in  which  the  par  of  exchange  is  2240  paper  rubles^ 
£100  sterling. 


304  SUPPLEMENT. 

• 

FRANKFORT-ON-THE-MAINE. 

MONEY  OF  ACCOUNT. — 1  rix  dollar— 90  krenzeT8=l|  florins = 
22£  batzen  =  360  hellers.  The  Prussian  money  is  used  for  the 
payment  of  duties  in  Frankfort,  and  in  all  the  States  of  the 
German  Customs-Union — the  value  of  1  Prussian  dollar  being 
fixed  at  105  kreuzers.  There  are  two  moneys  of  account  at 
Frankfort,  viz.,  Reichsgeld  or  24  Guldenfuss,  and  "Wechselzah- 
lung.  Reichsgeld  is  called  24  Guldenfuss  or  florin-foot,  from 
the  Cologne  mark  weight  of  fine  silver  being  valued  at  24  of 
these  florins.  WechselzaKlung,  or  exchange  reckoning,  is  de- 
duced from  the  estimation  of  the  carolin  at  9  florins  12  kreuz- 
ers in  Wechselzahlung,  the  value  of  the  same  being  11  florins  in 
24  Guldenfuss,  from  which  46  rix-dollars  W.  Z.=55  rix  dollars 
in24G.F. 

PAK  OF  EXCHANGE.— 148.2  batzeu  W.Z.  =  £l=$4.86f. 

1  rix-dollar  in  24  Guldenfuss =30. 4 7  pence  sterling. 
"      Wechselzahlung=36.43  " 

AUSTRIA. 

MONEY  OF  ACCOUNT. — 1  florin =60  kreuzers.  A  rix-dollar  is  1^ 
florins  or  90  kreuzers,  and  is  a  nominal  money  used  in  ex- 
changes but  not  in  accounts.  The  value  of  the  money  of 
account  is  that  called  Convention,  or  20  Guldenfuss,  in  which 
the  Cologne  mark  weight  of  fine  silver  is  supposed  to  bo 
coined  into  20  florins,  a  standard  only  T4T$  above  the  Wechsel- 
zahlung  of  Frankfort.  The  currency  of  Austria  is  of  both 
paper  and  metal.  The  paper  money,  called  Wiener-wahrung, 
or  Vienna  value,  is  at  a  fixed  discount  of  60$:  by  which  100 
florins  in  cash  are  equal  to  250  florins  in  W.  "W.  Bills  upon 
Vienna  are  generally  directed  to  be  paid  in  effective — that  is, 
in  cash — sometimes  mentioning  the  kind  (as  20  kreuzer-pieces, 
for  example),  to  guard  against  their  being  paid  in  paper  money 
of  the  depreciated  value. 

PAR  OF  EXCHANGE. — 9  florins  50  kreuzers =£1=84.86=-. 
1  rix-dollar  in  20  Guldenfuss  =  3 6. 5 6  pence  sterling. 

VENICE   AND   MILAN. 

MONEY  OF  ACCOUNT. — 1  lira  Austriaca=100  centisimi=20  soldi 
Austriaci.  The  lira  has  the  same  value  as  the  20  kreuzer-piece, 
or  the  third  of  an  Austrian  florin. 

PAR  OF  EXCHANGE. — 29  lire  52  cent.=£l,  or  1  lira=8id. 


SUPPLEMENT.  305 

TUSCANY. 

MONEY  OP  ACCOUNT.  —  1  lira  Toscana=100  centisimi=20  soldi 
di  Lira,  a  little  below  the  Venetian  standard. 

PAR  OF  EXCHANGE.  —  30.69  lire  =£1,  or  1  lira= 


BREMEN. 

MONEY  OF  ACCOUNT.  —  5  schwaren—  1  grote  ;  72  grotes=l  rix- 
dollar.  The  rix-dollar  is  valued,  in  gold,  from  the  old  French 
and  German  Louis  d'or,  at  the  rate  of  5  rix-dollars  to  1  Louis 
d'or. 

PAR  OF  EXCHANGE.  —  1  rix-dollar  =  3s.  3.4d.  sterling=S0.79£.  In 
the  U.  S.  the  quotations  of  exchange  on  Bremen  are  so  many 
cents  per  rix-dollar. 

CANADA. 

MONEY  OP  ACCOUNT.  —  1  pound  =20  shillings  =240  pence  =4  dol- 
lars =400  cents.  The  decimal  system  of  dollars  and  cents  has 
been  recently  introduced. 

PAR  OF  EXCHANGE.  —  The  Canadian  pound  (£),  as  represented 
by  their  paper  currency,  has  been  considered  equivalent  to  four 
dollars  U.  S.  currency.  But  the  recent  silver  coinage,  fur- 
nished that  province  by  England,  is  3f$  below  the  silver  coin- 
age of  the  U.  S.  in  value,  their  20  cent-piece  being  worth  only 
$0.1927;  and  as  the  U.  S.  silver  coinage  is  somewhat  below 
par,  taking  the  gold  coinage  for  the  standard,  we  may  con- 
clude that  the  par  of  exchange  between  Canada  and  the  United 
States  will  soon  be  104  cents  Canada  currency  =  6  1,  or  100 
cents  U.  S.  currency. 

UNITED  STATES. 

PAR  OF  EXCHANGE.  —  Gold,  or  its  equivalent,  being  the  cur- 
rency of  New  York  city,  and  paper  money  being  extensively 
used  throughout  the  States,  the  par  of  exchange  on  New  York 
city,  for  the  year  1860,  is  very  nearly  as  follows: 


New  England  States,     \%  prem.  \  Ohio,  Ky.,  and  Ind., 

New  York  State,  £$    '"      j  Detroit/ 

Baltimore,     -         -       Par.  Interior  Michigan,      \\% 


Philadelphia, 

Pit  tsburg"  par  funds,"    " 


"" 


currency 


20 


Iowa,  111.,  and  Wis.,  \\%  " 
Missouri,  -  -  \~  %  " 
New  Orleans,  -  Par. 


306 


SUPPLEMENT 


FOREIGN    COINS. 

Their  Weight,  Fineness,  and  Value,  as  Assayed  at  the  United  States  Mint. 

Remark. — The  basis  of  valuation  of  the  silver  coins  is  $1.21 
per  ounce  of  standard  fineness,  which  is  the  present  mint  price. 

GOLD  COINS. 


CouNTar. 

DENOMINATION. 

Weight. 

Fineness. 

Value. 

Australia  

Pound  of  1852  

Oz.  dec. 
0.281 

Thous. 
916.5 

D.  C.  3f. 

532  0 

Australia        .   .      .  . 

Pound  of  1855 

0  257 

9165 

4  85  0 

Austria  

Ducat  

0.112 

986 

2  28  0 

0.3G3 

900 

6  V7.0 

Belgium        .       . 

Twenty-five  francs. 

0  254 

899 

4  72  0 

Bolivia  

Doubloon  

O.S67 

870 

15  58  0 

Brazil  

20,000  reis  

0.575 

917.5 

1090  5 

Central  America.     . 

Two  escudors 

0  209 

853  5 

3  66  0 

Chili  

Old  doubloon  

0  867 

870 

15  57  0 

Chiii  

0.492 

900 

9  15.3 

Denmark 

Ten  thaler 

0  427 

895 

7  900 

Ecuador.  .        ... 

Four  escudors  

0433 

844 

7  60  0 

England  

Pound   or  sovereign,  new.  .  . 

0.256  7 

916.5 

4  86.3 

England 

Pound  average          . 

0  256 

915  5 

4848 

France  

Twenty  francs  new       . 

0.207  5 

899  5 

3  86  0 

France  

Twenty  francs,  average  

0  207 

899 

3  84.5 

Germany  North 

Ten  thaler       . 

0  427 

895 

7  900 

Germany  North 

Ten  thaler.  Prussian. 

0497 

(03 

8  00  0 

Germany,  South  
Greece  

Ducat..  

0.112 
0.185 

986 
900 

2.28.3 
3.45.0 

Hindostan 

Mohur     ...          . 

0  374 

916 

7  08.0 

Mexico     

Doubloon,  average  .... 

0  867  5 

866 

15,53.4 

Naples  

0.245 

996 

5.04.0 

Ten  guilders  

0.215 

899 

3.99.0 

New  Grenada 

Old  doubloon   Bogota 

0  8G8 

870 

15  61.7 

New  Grenada..  .  . 

Old  doubloon,  Popayan. 

0  867 

858 

15.39.0 

New  Grenada,  

0.525 

891.5 

9.67.5 

Peru  

Old  doubloon 

0  867 

868 

15.56.0 

Portugal  

Gold  crown  

0  308 

912 

5.81.3 

Rome  

2-J-  Scudi,  new  

0.140 

900 

2.60.0 

Russia  

Five  roubles  

0.210 

916 

3.97.6 

Sardinia  

Spam  

100  reals  

0  268 

896 

4.96.3 

Sweden  

Ducat                    . 

0  111 

975 

2.26.7 

Turkey  

100  piastres  

O.°31 

915 

4.37.4 

Tuscan\-.  .  . 

Sequin.  . 

0.112 

999 

2.30.0 

The  above  shows  the  intrinsic  relative  value,  as  compared  with 
the  amount  of  fine  gold  in  the  U.  S.  coin.  The  price  paid  at  the 
mint  would  be  \%  less. 


SUPPLEMENT. 


307 


SILVER  COINS. 


COUNTRY. 

DENOMINATION. 

Weight. 

Fineness. 

Value. 

Austria,         

Rix-dollar  

Oz.  dec. 
0902 

Thous. 
833 

D.C.M. 
1013 

Scudo  of  six  lire 

0  836 

902 

1  01  5 

Austria     .                .  . 

20  kreutzer 

0  915 

582 

16  8 

Five  francs.  .... 

0.803 

897 

96  8 

Bolivia  

Dollar  

0.871 

900.5 

1.05  4 

Bolivia   

Half  dollar   1830 

0433 

670 

38  5 

Bolivia  

Quarter  dollar   1830. 

0.216 

670 

19  2 

Brazil 

2  000  reis 

0  890 

918  5 

1  01  3 

Central  A.merica     .  . 

Dollar 

0866 

850 

97  3 

Chili     

Old  dollar.  . 

0.864 

908 

1  047 

Chili  

New  dollar  

0.801 

900.5 

97  0 

Denmark              .  . 

Two  ri<rsdaler 

0  927 

877 

1  09  4 

England  

Shilling,  new  

0.182.5 

924.5 

22  7 

England 

Shilling  average 

0  178 

995 

22  2 

France  

Five  francs,  average  .  . 

0.800 

900 

96  8 

Germany,  North  

Thaler  

0  712 

750 

71.7 

Germany    South 

Gulden,  or  florin 

0340 

900 

41  2 

Germany,  North  &  South  . 
Greece  rf  

2  thaler,  or  3^  guld  
Five  drachms  

1.192 
0.719 

900 
900 

1.44.3 

869 

Hindostan    .  . 

Rupee  .  . 

0374 

916 

46  0 

Japan  

Itzebu  

0.279 

991 

37  0 

Mexico 

Dollar   average 

0  866 

901 

1  04  9 

Naples 

Scudo  .... 

0  884 

830 

98  8 

Netherlands  

2i  guilder  

0.804 

944 

1  023 

Norway 

Specie-daler 

C  927 

877 

1  09  4 

New  Grenada  

Dollar  of  1357  

0803 

896 

968 

Peru 

Old  dollar 

0  866 

901 

1  04  9 

Peru  

Old  dollar  of  1855 

0  766 

909 

93  6 

Peru  

Half  dollar,   1835-'38.. 

0.433 

650 

377 

Portugal 

Silver  crown 

0  950 

912 

1166 

Rome  .    . 

Scudo  

0864 

900 

1  04.7 

Russia 

Rouble 

0  667 

875 

78  4 

Sardinia.    .      .            .... 

Five  lire      .  . 

0800 

900 

96  8 

New  pistareen  

0.166 

899 

20  1 

Sweden 

Rix-dollar 

1  092 

750 

1101 

Switzerland  

Two  francs  

Oo23 

899 

39  0 

Turkey 

Twenty  piastres 

0  770 

830 

86  5 

Tuscany..  . 

Florin.  .  . 

0.220 

925 

27.4 

308 


SUPPLEMENT. 


LINEAR,  OR  LONG  MEASURE. 

This  measure  is  used  to  define  distances  in  any  direction. 


12  inches 

3  feet 
5^  yards 
40  rods 

8  furlongs 


TABLE. 

(in.)  make  1  foot ft. 

"     1  yard yd. 

"     1  rod rd. 

"     1  furlong fur. 

"     1  statute  mile. .  mi. 


EQUIVALENTS. 


mi.   fur.      rd.  yd. 

1  =  8  =  320  =  1760 

1  =    40  =    220 

1  =        5 

1 


ft. 

=  5280 
—  660 
=  16 
=  3 
1 


in. 

=  63360 
—  7920 
=  198 
=  36 
=  12 


SCALE  OF  UNITS:— 12,  3, 


3  Jbarleycorns 

4  inches 
6  feet 

1.15  statute  miles 
3  geographic  miles 

60 

69^  statute         " 
360  degrees 


40,  8. 

ALSO: 

make  1  inch 
"  1  hand 
"  1  fathom 

"      1  geographic  mile . .  " 
"      1  league. 

"   ) 

„   j- 1  degree. 

"      the  circumference  of  the  earth. 


.used  by  shoemakers. 
.  "  to  measure  horses. 
.  "   to  measure  depths  at  sea. 
.  "          "         distances  " 


SQUARE  MEASURE. 

This  measure  is  used  to  compute  surfaces  or  areas. 


TABLE. 
144  square  inches  (sq.  in.)  make  1  square  foot 


9  square  feet 

30£  square  yards 

40  square  rods 

4  roods 
640  acres 


1  square  yard. .. 

1  square  rod 

1  rood 

1  aero 

1  square  mile 


EQUIVALENTS. 

eq.  mi.  A.     R.     eg.  rd.     sq.  yd.       sq.  ft. 
I  =  640  =  2560  =  102400  =  3097600  =  27878400 

1  =    4  =    160  =    4840  = 
1  =     40  =    1210  = 

1  = 


43560 
10890 


SCALE  or  UNITS  :— 144,  9,  30£,  40,  4,  640. 


.  sq.ft. 
.  sq.  yd. 
.  sq.  rd. 
.  E. 
.  A. 
.  sq.  mi. 

sq.  in. 

=  4014489600 

=    6272640 

=    1568160 

39204 

=      1296 
=       144 


SUPPLEMENT.  309 


SURVEYORS'  MEASURE. 

This  measure  is  used  to  compute  land  distances  and  areas.  A  Gunter's  chain, 
which  is  the  measure  used  by  surveyors,  is  four  rods  in  length,  and  consists  of  100 
links. 

TABLE    OF    LINEAR   DISTANCES. 

7.92  inches  (in.)        make  1  link I 

25  links  "      1  rod. rd. 

4  rods,  or  66  feet,    "      1  chain.. .  ch. 
80  chains  "      1  mile.. . .  mi. 

EQUIVALENTS. 


mi. 

ch. 

rd. 

I 

in. 

1  = 

80 

=  320  = 

8000 

= 

63360 

1 

=    4  = 

100 

= 

792 

1  = 

25 

— 

198 

1 

— 

7.92 

SCALE  OP  TT^ITS: — 7.92,  25,  4,  80. 

TABLE   OF  AREAS. 

625  square  links  (sq.  I)  make  1  pole P. 

16  poles  "      1  square  chain,  sq.  ch. 

10  square  chains  "      1  acre A. 

640  acres  "      1  square  mile. .  sq.  mi. 

36  square  miles  (6  miles  square)  "      1  township. . . .  Tp. 

EQUIVALENTS. 

Tp.  sq.  mi,    A.      sq.  ch.      P.  sq.  1. 

1  =  36  =  23040  =  230400  =  3686400  =  2304000000 

1  =   640  =   6400  =±  102400  =  64000000 

1  =     10  =     160  =  10000 

1  =      16  =  1000 

1  =  625 
SCALE  or  UNITS:— 625,  16,  10,  640,  36. 


CUBIC  MEASURE. 

This  measure  is  used  to  compute  the  contents  of  solid  substances ;  it  is  sometimes 
called  "solid"  measure. 

TABLE. 

1728  cubic  inches  (cu.  in.)  make  1  cubic  foot cu.fl. 

27  cubic  feet                       "      1  cubic  yard. . .  cu.  yd. 
16  cord  feet  "      1  cord  foot cd.fi. 

8  cord  feet,  or    ) 

••no      *-•?*.  1  cord  of  wood.,  cd 

128  cubic  feet        ) 

24f-  cubic  feet  "      1  perch Pch. 


310  SUPPLEMENT. 

LIQUID    MEASURE. 

This  measure  is  used  for  measuring  liquids ;  such  as  liquors,  molasses,  water,  etc, 

TABLE. 

4  gills  (gi.)  make  1  pint pt. 

2  pints  "      1  quart qt. 

4  quarts         "      1  gallon gal. 

31 }  gallons       "      1  barrel bbL 

2  barrels       "      1  hogshead MuL 

EQUIVALENTS. 

hhd.         III.  gal.  qt.  pt.  gi. 

1     =     2     =     63     =     252     —     504  =     2016 

1  =     31 J  =     126     —     252  =     1008 

1     =         4=         8  =         32 
1=2=  8 

1  =  4 

SCALE  or  UNITS: — 4,  2,  4,  31£,  2. 

ALSO, 

36  gallons     make  1  barrel  of  ale,  beer,  or  milk. 
54       "  "      1  hogshead      "  " 

42       "  "      1  tierce. 

2  hogsheads   "      1  pipe,  or  butt. 

2  pipes  "      1  tun. 

DRY  MEASURE. 

Used  for  measuring  articles  not  liquid;  as  grain,  fruit,  salt,  etc. 
TABLE. 

2  pints  (pt.)  make  1  quart qt. 

8  quarts  "      1  peck '  pk. 

4  pecks  "      1  bushel bu. 

36  bushels         "      1  chaldron. . .  ch. 
EQUIVALENTS. 


ch. 

^    

bu. 

36  = 

pk. 
144 

ft 

=  1152 

pt. 
=  2304 

1  = 

4 

=    32 

=    64 

1 

=     8 

=    16 

1 

=     2 

SCALE  OF  UNITS: — 2,  8,  4,  36. 

AVOIRDUPOIS  WEIGHT. 

Used  to  weigh  all  coarse  articles ;  as  hay,  grain,  groceries,  wares,  etc.,  and  aU 
metals,  except  gold  and  silver. 

TABLE. 

16  drams  (dr.)          make  1  ounce oz. 

16  ounces  "      1  pound Ib. 

25  pounds  "      1  quarter qr. 

4  quarters                  "      1  hundred  weight,  cwt. 
20  hundred  weight     "      1  Ton T. 


S  U  P  P  L  E  M  E  N  T.  311 


EQUIVALENTS. 

T. 

1 

ewt. 
=    20 

gr. 

=     80 

W. 
=     2000     = 

oz. 
32000 

dr. 
=    512000 

1 

=       4 

—       100    = 

1600 

=       25600 

1 

=         25     = 

400 

=        6400 

1     = 

16 

=           256 

1 

=            16 

£CALE  OP  UNITS:— 16,  16,  25,  4,  20. 

TROY  WEIGHT. 

For  weighing  gold,  silver,  jewels,  and  liquors. 

TABLE. 

24  grains  (gr.)         make  1  pennyweight . .  pwt. 
20  pennyweights    ,  "      1  ounce — . . . . .  oz. 

12  ounces  "      1  pound Ib. 

EQUIVALENTS. 
II.  oz.  pwt.  gr. 

1     =     12     =     240     =     5760 
1    as      20    =      480 
1     =         24 
SCALE  OP  UNITS: — 24,  20,  12. 

APOTHECARIES'  WEIGHT. 

Used  by  apothecaries  and  physicians  in  mixing  medicines. 

TABLE. 
20  grains  (gr.)  make  1  scruple. ...  3 

3  scruples  "      1  dram 3 

8  drams  "      1  ounce § 

12  ounces  "      1  pound 5> 

EQUI  VALEN  TS. 

fc  §  S  »  I* 

1      =     12     =     96     =     288  =  5760 

1     =       8     =       24  =  480 

1     =         3  =  60 

1  =  20 

SCALE  OP  UNITS: — 20,  3,  8,  12. 

TIME  MEASURE. 

Used  to  denote  the  passage  of  time. 

TABLE. 
60  seconds  (sec.)  make  1  minute ....  m. 

60  minutes  "      1  hour hr. 

24  hours  "      1  day da. 

7  days  "      1  week wk. 

365^  days  "      1  year yr. 

100  years  "      1  century C. 


312  SUPPLEMENT. 


EQUIVALENTS. 


I  = 


1     =  60 

Note. — It  is  customary  to  reckon  4  weeks  to  the  month,  and  1 2  months  to  thd 
year,  but  as  this  only  approximates  the  truth  we  have  omitted  it.  Twelve 
calendar  months  make  a  year,  but,  these  months  are  not  of  regular  length,  as  the 
following  table  will  show: — 


wk. 

da. 

hr. 

min. 

sec. 

52  = 

365^  = 

8766 

— 

525960 

= 

31557600 

1  — 

7  = 

168 

= 

10080 

= 

604800 

1  = 

24 

— 

1440 

— 

86400 

1 

= 

60 

= 

3600 

1.  January  has  31  days. 

2.  February   "    28      " 

3.  March        "31      " 

4.  April          "    30      " 

5.  May  "    31       " 

6.  June          "    30      " 


7.  July  has  31  days. 

8.  August         "31       " 

9.  September    "    30      " 

10.  October        "    31      " 

11.  November    "    30      " 

12.  December     "31      " 


The  year,  as  indicated  above,  would  consist  of  365  days.  This  is  the  length 
of  the  common  year.  Once  in  four  years,  however,  one  day  is  added  to  Febru- 
ary, making  366  days ;  and  thus,  each  year  averages  365^  days.  The  longest 
year  is  called  Bissextile,  or  Leap  year.  The  leap  years  are  all  exactly  divisible 
by  4. 

CIRCULAR  MEASURE 

Is  used  to  determine  localities,  by  estimating  latitude  and  longitude;  also,  to 
measure  the  motions  of  the  heavenly  bodies,  and  computing  differences  of  time. 
All  circles,  of  whatever  dimensions,  are  supposed  to  be  divided  into  the  same  num- 
ber of  parts — as  quadrants,  signs,  degrees,  etc.  It  witt,  therefore,  be  evident,  that 
there  can  be  no  "fixed  "  dimensions  of  the  units  named. 

TABLE. 

60  seconds  (")  make  1  minute. . . .  ' 

60  minutes  "  1  degree. . . .  ° 

30  degrees  "  1  sign. .....  S. 

12  signs,  or  360  degrees    "  1  circle 0. 

EQUIVALENTS. 

C.  S.  °  " 

1     =     12     =     360     =     21600     =     1296000 
1     =       30     =       1800     =       108000 
1     =  60     =  3600 

1     =  60 

SCALE  OF  UNITS: — 60,  60,  30,  12. 


SUPPLEMENT. 


313 


MISCELLANEOUS   TABLE. 


12  units 

make 

1   dozen. 

12  dozen 

<( 

1    gross. 

12  gross 

« 

1   great  gross. 

20  things 

it 

1    score 

100  pounds 

a 

1   quintal  offish. 

196  pounds 

« 

1  barrel  of  flour. 

200  pounds 

ll 

1   barrel  of  pork. 

18  inches 

II 

1    cubit. 

22  inches  (nearly) 

i; 

1   sacred  cubit. 

14  pounds  of  iron  or  lead 

" 

1   stone. 

2H  stones 

(( 

1   Pig. 

8  pigs 

a 

1   fother. 

BOOKS  AXD   PAPER, 

Barnes  of  different  sizes  of  paper  made  by  macJiinery. 


Double  imperial,         32  by  44    inches.     Imperial, 

22    by  32    inches. 

Double  Super  Royal,  27  by  42        " 

Super  Royal, 

21    by  27 

Double  medium,         23  by  26        " 

Royal, 

19    by  24        " 

"                       24  by  37  £      " 

Medium, 

18J  by  23£      " 

"                       25  by  38        " 

Demy, 

17    by  22 

Royal  and  Half,          25  by  29        " 

Folio  Post, 

16    by  21 

Imperial  and  Half,      26  by  32        " 

Foolscap, 

14    by  W        " 

Crown,   15  by  20  inches. 
A  sheet  folded  in  2  leaves  is  called  a  folio. 


12 
18 
24 
32 


a  quarto,  or  4to. 
an  Octavo,  or  8vo. 

a  12mo. 
an  18mo. 
an  24mo. 

a  32mo. 


In  estimating  the  size  of  the  leaves,  as  above,  the  double  medium  sheet  is 
taken  as  a  standard, 


24  sheets 

20  quires 

2  reams 

6  bundles 


make 


quire. 
ream. 
bundle. 
bale. 


314 


SUPPLEM  ENT. 


PRACTICAL  HINTS  FOR  FARMERS. 

1.  MEASURING  GRAIN.—  By  the  United  States 
standard,  2150  cubic  inches  make  a  bushel.  Now, 
as  a  cubic  foot  contains  1728  cubic  inches,  a  bushel 
Is  to  a  cubic  foot  as  2150  to  1723  ;  or,  for  practical 
purposes,  as  4  to  5.  Therefore,  to  convert  cubic 
feet  to  bushels,  it  is  necessary  only  to  multiply 


by  |.  EXAMPLE.  —  IIovv  much  grain  will  a  bin  hold 
which  is  10  fe»-t  Ions,  4  feet  wide,  and  4  feet  deep? 
Solution.—  10  x  4  x  4=160  cubic  feet.  160  x  f  =128, 


the  number  of  bushels. 

To  measure  grain  on  the,  floor.  —  Make  the  pile 
in  form  of  a  pyramid  or  cone,  and  multiply  tho 
area  of  the  base  by  one-third  the  height.  To  find 
the  area  of  the  base,  multiply  the  square  of  its  di- 
ameter by  the  decimal  .7854.  EXAMPLE.—  A  coni- 
cal pile  of  grain  is  8  feet  in  diameter,  and  4  feet  high, 
how  many  bushels  does  it  contain  ?  Solution.—  The 
square  of  8  is  64;  and  64  x.  7854  x  J  =83.776,  the 
number  of  cubic  feet.  Therefore, 

83.776  x  4  =67.02  bushels.    Answer. 

2.  To  ASCERTAIN  THE  QUANTITY  OF  LU.MBER  IN  A 
Loo.  —  Multiply  the  diameter  in  inches  at  the  small 
end  by  one-half  the  number  of  inches,  and  this 
product  by  the  length  of  the  log  in  feet,  which  last 
product  divide  by  jl2.     EXAMPLE.—  How   many 
feet  of  lumber  can  bf  made  from  a  log  which  is  36 
inches  in  diameter  and  10  feet  long?    Solution.  — 
36  x  18=643;  648x10=6480;  64SO-f  12=540.  Am. 

3.  To  ASCERTAIN  TIIB  CAPACITY  OP  A  CISTERN 
OR  WELL.—  Multiply  the   square  of  the  diameter 
in  inches  by  the  decimal  .7854,  and  this  product  by 
the  depth  in  inches;  divide  this  product  by  231, 
and  the  quotient  will  be  the  contents  in  gallons. 
EXAMPLE.  —  What  is  the  capacity  of  a  cistern  which 
is  12  feet  deep  and  6  feet  in  diameter  >   Solution.— 
The  square  of  72,  the  diameter  in  inches,  is  5184; 
51S4  x  .7854=4071.51  ;  4071.51  x  144=586297.44,  the 
number  of  cubic  inches  in  the  cistern.    There  are 
231  cubic  inches  in  a  gallon,  therefore,  586297.44 


-•-231=2538+,  gallons.    To  reduce  the  number  of 
gallons  to  barrels,  divide,  by  31£. 

4.  To  ASCERTAIN  THE  WEIGHT  OK  CATTLH  BY 
MEASUREMENT. — Multiply  the  girth  in  feet,  by  the 
distance  from  the  bone  of  the  tail  immediately  over 
the  hinder  part  of  the  buttock,  to  the  fore  part  of 
the  shoulder-blade  ;  and  this  product  by  31,  when 
the  animal  measures  more  titan  7  and  lean  than  9 
feet  in  girth;  by  23,  when  less  than  1  and  more 
man  5;  by  16,  when  leafs  than  5  and  more  than 
3  ;  and  by  11,  when  lens  than  3.    EXAMPLE.— What 
is  the  weight  of  an  ox   whose  measurements  are 
as  follows;   girth,  7  feet  5  inches;  length,  5  feet 
6  inches? 

Solution.— 5i.x7T82=405i;  40-^x81  =  1264  +  .  AM. 
A  deduction  of  one  pound  in  20  must  be  made  for 
half-fatted  cattle,  and  also  for  cows  that  have  had 
calves.  It  is  understood,  of  course,  that  such 
standard  will  at  best,  give  only  the  approximate 
weight. 

5.  MEASURING   LAND.— To  find  the  number  of 
acres  of  land  in  a  rectangular  field,  multiply  the 
length  by  the  breadth,  and  divide  the  product  by 
160^  if  the  measurement  is  made  in  rods,  or  by 
43560  if  made  in   fret.      EXAMPLE.— How  many 
acres  in  a  field  which  is  100  rods  in  length,  by  75 
rods  in  width?      Solution.— 100x75=7500 ;  7500 
-*-160=46fi.    Answer.     To  find  the  contents  of  a 
triangular  piece  ot  land,  having  a  rectangular  cor- 
ner, multiply  the  two  shorter  sides  together,  and 
take  one-half  the  product. 

6.  MEASUREMENT  OF  HAY.— 10  cubic  yards  of 
meadow  hay,  weigh  a  ton.     When  the  hay  is  taken 
out  of  old,  or  the  lower  part  of  large  stacks,  8  or  9 
cubic  yards  will  make  a  ton.     10  or  12  cubic  yards 
of  clover,  when  dry,  make  a  ton. 

Hay  stored  in  barns,  requires  from  3M  to  400 
cubic  feet  to  make  a  ton.  if  it  be  of  medium  coarse- 
ness, and  greater  or  less  quantity,  varying  from 
300  to  500  solid  feet,  according  to  its  quality. 


OF 


MONEY,  WEIGHT,  AND  MEASURE, 


PRINCIPAL    COMMERCIAL    COUNTRIES    IN    THE    WORLD. 


WE  are  indebted  to  the  Publishers  of  "  WEB- 
BTEK'S  COUNTING  HOUSE  DICTIONARY"  for  the  use 
of  the  following  admirably  arranged  Tables,  which 
will  be  found  of  great  value  for  reference.  The 
tables  have  been  prepared  with  much  care  and 
may  be  relied  upon  as  correct 

GREAT    BRITAIN. 

(Principal  Commercial  City,  LONDON.) 

Money. 

The  national  Currency  of  Great  Britain  is  called 
Sterling  Money — thus  we  say,  so  many  pounds 


sterling.  The  Pound  Sterling  is  represented  by  a 
gold  coin  called  :\  Sovereign,  and  its  custom-house 
value  in  the  United  States  is  fixed  by  law  at  $4.84. 
The  intrinsic  value  of  the  Sovereign  varies  some- 
what, depending  on  the  date  of  the  coinage.  Vic- 
toria sovereigns  are  worth  the  most,  as  being  of  the 
latest  coinage;  those  of  William  IV. or  Goorge  III. 
less,  as  more  worn.  The  commercial  value  of  the 
pound  sterling  varies,  like  merchandise,  according 
to  demand;  $4.84  is  that  on  which  duties  are 
charged.  Thus  if  you  buy  a  bill  of  goods  in  Lon- 
don of  £100,  on  which  the  duty  in  this  country  is 
25  per  cent.,  and  import  them,  you  pay  at  tho 
Custom  house  25  per  cent,  on  $484,  or  $121.  What 


STTPPLEM  ENT, 


315 


Is  called  the  par  value  of  the  pound  sterling  in 
the  United  States  is  $4.44  4-9.  The  par  value  of 
the  pound  in  London,  in  American  currency,  is 
$4.Sd.  The  difference  between  the  par  value  of 
the  pound  sterling  in  this  country  ($4.44  4-9)  and 
the  actual  value  to  us  here,  at  the  time,  of  a  pound 
sterling  in  London,  is  called  the  Exchange.  Thus, 
if  exchange  on  London,  ia  New  York,  is  9  per  cent., 
a  pound  sterling  is  worth  $4.44  4-9,  and  9  per  cent. 
added,  or  $4.84.  If  7  per  cent.,  of  course,  less;  if 
lj  per  cent.,  more. 

freight  bills  for  goods  by  ehip  are  payable  at 
f4.80  the  pound,  which  is  8  per  cent  on  $4.44  4-9. 
Exchange  on  London  is  usually  7  to  10  per  cent,  in 
New  York,  i.  e.  a  pound  sterling  in  London  is 
worth  $4.44  4-9  and  7  to  10  per  cent,  additional,  in 
New  York,  nearly. 

In  the  following  Tables  we  give  the  pound  at 
f4.S4,  it  being  understood  that  its  commercial 
Value  ia  sometimes  higher  and  sometimes  lower. 

4  farthings,  qr.  =  1  penny,     d. 

12  pence  =  1  shilling,    «. 

20  shillings  =  1  pound,    £. 

A  sovereign,  =  2)  shillings. 

A  guinea  =  21        " 

A  crown  =  5  *     " 

A  groat  =  4  pence. 

The  farthing  is  an  imaginary  coin  ;  the  penny, 
copper;  the  sixpence,  shilling,  and  crown,  silver; 
Eovcreiprnand  guinea,  gold. 

The  EnglislTTables  of  Weights,  Measures,  Time, 
Ac.,  are  the  same  essentially  as  the  American. 

The  value  of  the  Pound  Sterling  ia  the  following 
Tables  ia  put  at  $4.84. 


AUSTF.IA. 
(Chief  'Commercial  City,  YICX 
Money.  In  Silver. 


fl.  krt. 
10    0 

0  30 

0    2* 

70 

4  40  or  ducat 


£    s.   d.  $  c.  m. 

=     1     0    0  =  4  II  0 

=     010  =  0242 

=     0    0    1  =  0  C2  02-13 

=     0  13    6  =  3  26  7 

=     094  =  2  25  8  8-12 


1  0  silver  florin          =020     =     0434 

2  0  or  1  dollar  =     040     =     09(38 

0  20  or  1  zwanzigcr    =     008     =     0131  4-12 
1  florin  is  equal  to  CO  kreutzers. 

Taper  currency  is  depreciated  now  from  25  to  C5 
per  cent. 

"Weights  and  Measures. 
AUSTRIAN*.  ENGLISH. 

100  commercial  Ibs.     =  123.6  Ibs.  avoirdp. 

1  staro      ..         ..         =  2.34  Winch,  bush. 

IpoloHick         ..         =  0.861     ditto 

1  cimer    ..         ..         =  15  wine  gallons 

Ibarilc    ..         ..         =  173|       ditto 

1  ell  woolen  measure  =  26.6  in. 

1  ell  silk..         ..         =  25.2  ia. 

Or  njore  particularly — 

Weight. 

ENGLISH. 
123.6  Ibs.  avoirdp. 
=     4  vindlinge 
=     4  unzen 
=     2  loth 
=    4  quintl. 
=     20  Ihs. 
=     275  Ibs. 


AUSTRIAN*. 

100  commercial  Ibs.     = 

lib. 

1  vindlingo 

1  unzen  .". 

lloth       .. 

1  stone    .. 

1  sanae    . . 


Measure. 

1  foot          =     12i  inches 
1  nult        =      • 


Grain. 

C4  moasel    =      1    metz 
SJmetz       =       1    muta 
1  muth      =     5o£  bush.  Eng. 

EAVAEIA  AND  BADIIT. 
(Principal  Commercial  City,  AUGSBTTBG.) 

Honey. 

fl.  krt  £   8.    d.      $  c.    m. 

12    »at  par   ..         ..         =  1    0    0  =  4  84  0 
036  ..         ..         =010  =  0242 

03  ..         ..         =001=0  02  0  2-12 

10  0  gold  10  guildr.  piece  =  0  16  8  =  4  08  34-12 
5  0  gold  5  do.  do.  =0  8  4  =  2  01  6  8-12 
3  30  silver  3f  flor.  piece  =  0  5  10  =  1  41  1  S-12 
5  35  or  ducat  ..  =09  3  =  2  23  8  6-12 
2  42  or  crown  thaler  =0  4  4  =  1048  8-12 
10  ..  ..  =018  =  0  40  3  4-12 

1  florin  is  equal  to  CO  kreutzers. 

Books  are  kept  in  Gulden  a  CO  krentzer  of  the  20 
grulden  fuss,  so  called  because  the  Cologne  mark  of 
line  silver  is  worth  only  2  )  fl.  Augsburg  currency, 
while  all  other  South  German  States  reckon  on  thd 
24  gulden  fuss. 

Coix.—  Gold    (old).     1    Caroline=li>.    <kZ.    En- 

glish =$4.44. 

i  caroline=9s.  8*7.  English  =  $2.22. 
1  double  max  d'or=24*.  4d.  English  =  $5.84. 
1  max  d'or=12s.  2d.  English  =  $2.92. 
1  ducat  (new)=9s.  4d.  English  =$2.24. 

Silver  pieces  of  S|  gulden,  1  gulden.  $  pnlden,  1 
kreuUer,  3  kreutzer,  all  in  the  24  gulde 


1  ponnd=5GO  grammes  French=lJ  pound   avoir- 

dupois. 

1  cwt.=100  pounds=3,200  loth=12.8nO  qnent 
1  Ausrsburg   marc=16  loth  =64  quent=25G  pfen- 

ning=3,643  grains  troy  English. 

Measure. 

The  foot  =11  1  inches  English. 
1  ruthe=U  feet=120  zoll  or  inches=1440  lines. 
1  ell=2  41-48  feet  =83!-  inches  English. 
1  klafter=6  feet=5=  feet  English. 

FOR  COBS.—  1  6cheffel=6  bushels  1  gallon  En- 
glish. 

1  scheffel=6metz=12  viertel=48  maas. 
FOB  LIQUOES.—  Wine,  1  eymer=6o  inaaa. 
Beer,  1        "     =6^    •• 
1  maas=lj  pints  English. 


BELGIUM. 

(Principal  Commercial  City, 
Money  (at  par). 


fr.  cts. 

25  0 

1  25 

0  10 


£  s.  d.      $  c.    m. 

=  1  0  0=^4840 

=0  1  0  =:  0  24  2 

0  0  1  =  0  02  0  2-12 


25    Oorl  gull  Leopold  =  0  19  1)  =  4  79  98-12 
10     0  or  Id  Irane  piece     =0     7  10  =  1  8958-12 
5    Oor    5  franc  piece     =0    3  11   =  094710-12 
10  ..         ..         =00    9|=  0  19  17-12 

1  franc  is  equal  to  100  centimes. 
"Weights  and  measures  the  same  as  in  Franc*. 


816 


SUPPLEMENT. 


BRAZILS. 
(Principal  Commercial  City,  Eio  DE  JANEIRO.) 

Money. 

reis.  £   s.    d.       $  c.    m. 

6400  or  gold  piece  =  1  15    9  =  8  65  1  6-12 

4000  or  gold  piece  of          =100  =  4  84  0 
1200  or  silver  piece  of       =04    2  =  1  00  8  4-12 
960  "  =  0    4    1  =  0  98  0  4-12 

640  "  =  0    2    9  =  0  66  5  6-12 

820  "  =  0    1    4  =  0  32  2  8-12 

200  "  =  0    0    8  =  0  16  1  4-12 

1  mil  reis  is  equal  to  1000  reis. 
The  unit  is  the  reis,  as  in  Portugal. 
Com.— Gold  dobra  a  12,800  reis= $18.00. 
Meia  dobra  a  6,400  reis =$9.00. 
Moeda  a  4oOO  reis=$5.75. 

Silver.— Pieces  of  1200  reis=$1.00. ;  400  reis=$0.83. 
Pieces  of  1«0  rcb=$o.v/8. 

Bank  Notes  are  worth  less  than  specie  "by  about 
one  third. 

Exchange  on  London,  SOd.  sterling  per  milrea  in 
bank  notes. 

Exchange  on  Paris,  fr.  3.15  to  fr.  3.20  per  1000 
reis. 

Weight 

1  quintal =4  arrobas  a  82  arratels,  (pounds.) 
1  arratel  (lb.)  =  ll^-  oz.  avdp. 
1  quintal=9H  lb.  avdp. 
Gold  and  silver  weight  is  the  arratel  a  2. 
Marcos  a  8  oncas  a  8  oitavas  a  72  granos. 
1  ma'rco=7  oz.  7  4-7  dwts.  troy. 
Diamonds,  emeralds,  rubies,  pearls,  &c.  are  sold 
by  the  quilate.  Topazes  by  the  oitava  a  3  escrupu- 
losa  3  quilates  a  4  granos. 

1  oitava=l"oz.  19  9-10  dwts.  troy. 
1  quilate=4  13-30  dwts.  troy. 

Measure. 

1  pe  (foot)  1=  foot  Eng. 
1  paltno=9i  inches  Eng. 
1  braca=2  varas=8£  covades=10  palmas, 
1  braca=2;  yards  Eng. 


1  legoa(mile)=4|  miles  Eng. 
CORN,  EICE,  Corn 


)FFEE,  &c.—l  mayo=15  fanegas, 
each  i'anega=4  alqueires. 

1  mayo=22i  bushels  Eng. 
1  fanega=ll  ;  gall. 
WINE. — The  same  as  in  Portugal. 

BREMEN. 

(One  of  the,  four  Free  Cities  of  Germany?) 

Money. 

rigdl.  grosch.  £   B.    d.        $  c.    m. 

66  ..         ..         =100=4  84  0 

024  ..         ..         =010  =  0  24  2 

1    0  or  gold  rigxd.nl.     =0    3    4  =  0  80  6  8-12 
0  86  or  36  groat  piece  =0    1     6  =  0  86  3 
5  24  or  Louis-d'or         =  0  16    0  =  3  87  2 
1  thaler  is  equal  to  72  groten. 

BRUNSWICK  AND  HANOVER. 

(Principal  Commercial  Cities,  BRUNSWICK  and 
HANOVER.) 

Money. 

tl.  grs.  pfci.  £   B.    d.      $  c.    m. 

6  16  0  ..  ..  =  1  0  0  =  4  84  0 
080  ..  ..  =010  =  0  24  2 
0  0  10  ..  ..  =  0  0  1  =  0  d2  02-12 

10    0    0  dble.  Georged'or  =  1  12    4  =  7  72  48-12 

6    0    0  or  single    "         =  0  16    2  =  8  91  24-12 

100         ..         ..         =080  = 

0    1    0  or  12  pfennings   =00    1±=  0  02  5  5-24 

1  thalur  is  equal  to  24  groschen. 


CB3NA. 

(Principal  Commercial  City,  CANTON.} 
Money. 

The  Chinese  reckon  in  taels,  a  10  mace,  a  10  can- 
darin,  a  10  cash. 

1  tael  =  6s.  6rf.  =  $1.56. 

COIN.—  They  only  have  the  cash  or  li.  All  other 
are  imaginary.  They  use  the  piasters  of  Spain  at 
72  candarins.  The  East  India  Company  take  the 
tael  only  at  6s.  720  taels=  1,000  dollars  of  Spain. 

The  exchange  on  London  is  4s.  8d.,  more  or  less, 
for  one  Spanish  dollar. 

Weight. 

1  pecul=100  cattys  (gin),  a  16  taels  (lyang),  a  10  mazas 

(tachen),  or  lo  candarins  (tv/in),  a  10  cash  (li). 
1  pecul     =  133}  pounds  avoirdupois. 
1  catty      =  li  pound 
1  tael        =  lj  ounce  " 

1  catty  (also    the  weight  for  gold  and  silver)  =1 

pound  7  3-5  ounces  troy  English  ;  1  tael=579  4-5 

grains  troy  English. 

The  assay  of  gold  and  silver  is  done  by  100  parta 
called  toques.  Silver  must  be  80-100  pure. 

Pleasure. 

The  covid=14|  inches  English. 
1  covid=10  punts. 

The  Chinese  use  four  different  feet: 
Tor  mathematics    =  13^  inches  English. 
For  builders  =  121-15 

For  engineers          =  12|  " 

For  trade  =  18j  " 

1  li=180  fathoms  of  10  feet  of  the  engineers=2-5 

of  an  English  mile. 

DENMARK 

(Principal  Commercial  City,  COPENHAGEN.) 

Money. 

rigsd.  ekil.  £    s.  d. 

9    16  ..         ..         =1 

44  ..         ..         =0 

8J  ..         ..         =  0 

50  or  1  Christian  d'or=  0  16  3 
0  or  \  species  silver  =0  44 
0  ..  ..  =  0  2  2 


00 
10 
0  1 


$.  c.  m. 
=4840 
=0  24  2 
=  0  02  02-12 
=  3  93  2  6-12 
=1048  8-12 
=  0  52  44-12 


0 
0 
7 
2 
1 

0  16  or  1  mark     ..         =0    0  4}  =  0  09  1 

1  rigsb.  diilor  is  equal  to  96  skillings. 

2  rigsbank  daler=l  hpecie-daler=3  mark  banco  in 

Hamburg. 

1  rigsbank  daler  =2*.  Sd.  English. 
1  skilling=l  farthing=half  a  cent  American. 

Bank  notes  in  specie  daler  are  freely  taken  —  100 
specie  daler  for  200  rigsbank  daler. 

They  draw  generally  on  Hamburg  at  sight  or  14 
days  after  date,  and  the  exchange  on  London  is  9J 
rigsbank  daler  for  £1  sterling.  Exchange  on  Pa- 
ris (rarely)  from  fr.  2.60  to  fr.  2.70  per  rigsbank 
duler. 

Weight. 

1  pound  =1  pound  If  oz.  avoirdupois. 
1  pound=16  ounces=82  loth=128  quenta- 
1  ship-pound  =320  pounds. 
1  last=16i  do.  or  52  cwt.  of  100  pounds. 
Gold  and  silver  are  sold  by  the  pound=2  marks 
=16  ozs.=512  orts=8192  es.    1  mark  =7  ozs.  4  1-5 
dwts.  Troy. 

Measure. 

1  foot=12*  inches  English. 
ell  =24  j  inches  English. 
mile=4*  miles  English. 
FOR  CORN.—  1  toende=8  skieps=S2  viertels. 
toende=80  gallons  4^  pints  English. 
skiep=3  gallons  6  \  pints  English. 
last  =22  toendes. 


STIPPLE  MENT. 


317 


EAST  INDIES. 

(Principal  Commercial  Cities,  BOMBAY,  BEXGAL, 

CALCUTTA,  and  MADRAS.) 
Tup's,  ann.  \>\.  £   s.   d.        $  c.  m. 

10      8      0  ..        =100=4840 

0      8      4  ..         =010=0242 

0      0      8  ..         =001=0  02  0  2-12 

1C      0      0  gold  mohur=  1    9    0=7018 
100  rupee  sicca  =0    1  10£  =  0  45  3  9-12 

0  8      0  half  rupee   =0    011^=022621-24 

1  rupee  is  equal  to  S  annas  or  90  pice. 

More  particularly — 

CALCUTTA.    Money. 
The  Company's  rupee=15-16  sicca  rupee=ls.  lid. 

=$0.40. 
1  rupee=16  anas;  1  ana=12  pice. 

COIN— Gold  :  1  mohur=15  rupees=33*.  2d.  En- 
glish=$3."2.6  4-12.  Silver :  1  sicca  rupee=2*.  En- 
glish =  $0.43.4 

Weight 

1  mannd  (factory  maund),  a  49  seers,  a  16  chattacks. 
1  maund=74  pounds  10  ounces  avoirdupois. 
1  seer=29j  ounces  avoirdupois.    The  bazaar  weight 

is  10  p.  ct.  heavier. 

1  sicca=10  massa  a  32  grains,  or  4  punkhos. 
1  sieca=173j  grains  troy  Engl. 

Measure. 

1  cubit=13  inches  English.    1  guz=l  yard  English. 
1  coss=4,000  cubits=lV  mile  English. 

Corn  is  sold  by  the  khahoon  of  40  maunds  or  16 
soallis  a  20  pallies.  1  pallie=9^  pounds  avoirdupois. 

MADRAS.    Money. 
The  same  as  Calcutta. 

Weight 

1  can<lv=2r>  mrrinds=16J  vis — 6,400  pollams. 
1  candy =500  Ibs.  avdp. 

Measure. 

Long  measure  the  same  as  Calcutta. 

FOR  CORX — 1  garee=400  mercals  a  8  puddys  or 
84  allocks. 
1  garee=135  bushels. 

BOMBAY.    Money. 

1  rupee=100  reas.     Value  as  in  Calcutta. 
Exchange  on  London,  2s.,  more  or  less,  i'or  1  Com- 
pany's rupee. 

Weight 

1  candy=20  maunds  a  43  seers  a  30  pice. 
1  candy =560  Ibs.  avdp. 

Measure. 

1  covid=18  inches  English. 
FOB  Coax— 1  candy =8  parahas  a  16  adowlies. 
1  candy=24^  bushels. 

EGYPT. 

(Principal  Commercial  City,  ALEXAITDBIA.) 

Money  (at  par.) 

piast.  par.  £  s.    d.       $  e.  m. 

97    20  . .         . .         =  1    0    0  =  4  84  0 

50  ..         ..         =010=0242 

017  ..         ..         =001=0  02  0  2-12 

5)  0  gold  new  sequin  =  0  10  4  =  2  50  0  8-12 
13  0  silver  new  piast  =0  3  4  =  0  8:-)  6  8-12 
4  0  silver  grush  =0  1  2=0  23  2  4-12 

1      0  piastre        ..        =00    21=00505-12 
Wholesale  payments  are  made  in  purses  of  500 
current  piasters,  chiefly  in  Span,  dollars  or  piasters. 
1  Sp.  dollar =20  Egypt,  piust. 


1  piaster  in  Alexandria  has  40  medinis  or  paras,  or 

100  good  or  12J  current  aspers. 
In  Cairo  1  piaster=8o  aspers  or  33  paras. 

COIN.— Ducatillo  a  10,  griscio  a  30,  piaster  a  40, 
mahouib  a  90,  and  zumabob   a  120  paras.     Also, 
zenzerli  a  107,  and  mecchini  a  146  zedinis. 
Cotton  is  sold  by  cantaros.    1  cantaro=115  Ib.  Eng. 
Coffee  and  Cotton  are  invoiced  in  Span,  dollars. 
Other  goods  in  Egyptian  Piasters. 

Exchange  on  London,  80  piasters,  more  or  less, 
for  $1  sterlg. 
Exchange  on  Paris,  315  a  320  per  fr.  ICO. 

Weight 

1  cantaro  a  100  rotoli. 

The  rotoli  differ.  There  are  rotolo  forforo  = 
15  oz. ;  rotolo  zauro  =  33V  oz. ;  rotolo  zadino  =•- 
21 5-16. ;  rotolo  mina=26  5-7  oz. 

The  quintal  of  coffee  in  Cairo=1033-5  Ib.  Eng. 
1  oka=400  drachmas  a  16  carat  a  4  grain. 
1  oka=3  Ib.  2  oz.  17  2-5  dwt.  troy. 
1  drachma =1  dwt  22£  grs. 

Measure. 

lpik=264-5in.  En?. 
FOB  COBX.— 1  rebebe=36  galls.  Eng. 
1  kisloz=39  galls.  Eng. 

FRANCE. 

(Principal  Commercial  City,  PAEIS.) 

Money  (at  par.) 

frs.  cts.  .    £   s.   d.      $  c.  m. 

25      0  ..         ..         =100=4840 

1    25  ..         ..         =  0    1    0  =024  2 

0    10  . .         . .         =001=0620  2-12 

20      0  or  gold  Napoleon  =  0  16    0  =  3  87  2 
5      0  or  silver    do.        =  0    4    0  =  0  96  8 
10        do.          . .         =00    9^=  0  19  1  7-12 
0    10  . .         . .         =00    l"=  0  02  0  2-12 

1  franc  weighs  5  grammes=100  centimes. 
Coix.— Gold  pieces  of  100,  40,  20  and  10  francs. 

Silver  pieces  of  5,  2, 1,  £  and  £  francs. 
Bank  notes  of  500  and  1000  francs. 
Exchange  on  London,  fr.  25.50  for  £1  sterlg. 
Exchange  on  New  York,  fr.  5.25  to  5.30  for"$l. 

Weights. 

Milligramme  =  0.0154  grs. 

Centigramme  =  0.1543 

Decigramme  =  1.5434 

Gramme    ..  =         15.4340 

Decagramme  =        154.3420 

or  5-64  drams  avoirdupois. 
Hectogramme       . .  =  32.154  oz.  troy, 

or  3-527  oz.  avoirdupois. 
Kilogramme =2  Ibs.  8  oz.  3  dwt.  2  grs.  troy, 
or  2  Ibs.  3  oz.  4652  drams  avoirdupois. 
Myriogramme      . .  =  26.795  Ibs.  troy, 

or" 22-0485  Ibs.  avoirdupois. 
Qnintal=l  cwt.  3  qrs.  25  Ibs.  nearly. 
Millier  or  bar =9  tons  16  cwt.  3  qrs.  12  Ibs. 
The  weight  of  1  cubic  centimetre  of  pure  water 
is  taken  as  the  foundation.    It  is  called  gramme. 
1  myriagramme-10  kilogr.=100  hectogr.=1000de- 

cagr.= 10,000  grammes. 
1  gramme=10  decigr.=100  centigr.=1000  milligr. 

1  eramme=152-5  grains  troy, 
or  the  kilogr. =15434  grains  troy. 
873J  gramrnes=l  Ib.  troy. 
453  3-5  grammes=l  Ib.  avdp. 
1  kilogr.  =2  Ib.  3*  oz.  avdp. 
1  quintal=100  kilogr. =22Ci  Ib.  avdp. 


318 


SUPPLEMENT. 


Measures. 

Long  Measure, 

FRENCH.  ENGLISH. 

Millimetre         ..         =         0.08937  in. 
Cenliuietre  =         0.89371 

Decimetre  =         8.93710 

Jleti-t*     ..  =       89.37100 

Decametre  =       32.S(i9l6  feet 

Hectometre  =      828.09167 

Kilometre  =    11,93.63890  yds. 

Myriometre         .         =  10936.3S900 

or  6  miles,  1  furlong,  28  poles. 
1  myriametre=10  kilometres=lUOhectoinetres= 
1000  Decam= 10,000  Metres. 

1  metre=10  decimetres=100   centimetres =1000 
millimetres. 

The  metre  is  the  10,000,000th  part  of  the  north- 
ern meridian  quadrant. 

1  metre=39  7-25  in.  En?. 
1  lieue=l  myriametre=6?  Eng.  miles. 
1  auue=l  1-5=47  l-6=in  Eng. 

Measures  of  Capacity. 

Millitre  ..         ..        =         0.06103  cub.  in. 

Centilitre          . .         =         0  61023 

Decilitre  ..         =         6.1028;) 

Litre*     ..         ..         =       61.02Su3 
or  21135  wine  pints. 

Decalitre  ..         =    610.28028  cub.  in. 

or  2-642  vino  gallons. 

Hectolitre          ..         =          8.531T  cub.  ft. 
or  26.419  wine  gallons,  22  imperial  gal- 
lons, or  2.839  Winchester  bushels. 

Kilolitre  . .         . .         =        85.3171  cub.  ft. 
or  1  tun  and  12  wine  gallons. 

Myriolitre          ..         =    353.17146  cub.  ft. 
FOR  WINE,  &c. — 1  litre =1  cubic  decimetre. 
1  myrialitre=10  kilol.=100  hectol.=1000  decal.= 
10,000  litres. 

1  litre=10  decil.=100  centil.=1000  millit.' 

1  litre=lf  pint  Eng. 

1  hectolitre =22  gallons  Eng. 

Superficial  Measure. 

Centiare  ..         ..        =  1 -I960  sq.  yds. 

Are  (a  sq.  decametre)  =        119-6C46 
Decare     ..         ..         =      1196-0460 
Hectare    ..         ..    .     =    11960-46C4 
or  2  acres,  1  rood,  85  perches. 


Solid  Measure. 


D6cistere 

Stere  (a  cubic  metre) 

Decastere 


3-5317  cub.  ft. 
&5-3174 
353-1741 


FRANKFORT  ON  THE  HATH". 
AND  THE  SOUTHERN  PARTS  OF  GERMANY. 

Money. 

1  gulden  a  63  kreuzers  a  4  pfennigc. 

1  gulden=$0.40=3  kreutzere=0.o2. 
COIN.— Ducats  a  $2.20. 

Pieces  of  8*  gulden  =  $1.40;  1  guld.  =  $0.40, 

and  half  gulden  =  $0.20. 
Old  pieces  of  2  2-5  gulden  =  $0.96 ;  i=$0.4S. 
Exchange  on  London,  12")  fl.,  m.  or  1.,  for  £10  stg. 

"  Paris,  fr.  2.10  a  2.15  per  fl. 


*  Metre  Is  the  fundamental  nnit  of  -weights  and 
measures ;  it  is  the  ten-millionth  part  of  the  one- 
fourth  of  the  terrestrial  meridian. 

t  A  cubic  decimetre. 


Money  (at  par). 

florins,  kr.  £    s.  <j.       $  c.  m. 

12        0        . .          . .       =  1    0  0  =  4  84  0- 

0      36        ..          ..       =0    1  0  =  0242 

9  4s  or  g.  Louis-d'or  =  016  1   =  3  89  2  2-12 
5      85  or  gold  ducat     =0    9  3  =  2  23  8  6-12 

42  or  silver  crown  =  0    4    4  =  1  04  8  8-12 

10  ••          -.       =018  =  0  40  3  4-12 
1  florin  is  equal  to  60  kreutzers. 

Weight. 

1  cwt.= 100  great  or  heavy  pds.= 108  small  or  light 

1  Ib.  heavy=17jj  oz.  avdp. 
1  Ib.  light=2  mark=321oth=12S  quent= 
512  pfennig=15  1-20  oz.  troy. 
1  mark=7  oz.  1C*  dwts.  troy. 
1  cwt.   of  100  heavy  or  1C8  light  Ibs.  =  111 

Ibs.  avdp. 

Gold  and  silver  are  sold  by  the  mark. 
1  curat  of  jewels=l  dwt.  7  5-7  gr.  troy. 

Measure. 

1  foot=ll}  in.  Engl. 
1  foot =12  zoll=144  lines. 
1  ell=21  5-9  in.  Engl. 
1  Francfort  Brabant  ell =2Tj  in.  Engl. 
FOR  CORN. — 1  maker  a  4  simmer  a  4  sechter  a  4 

gescheide. 

1  malter=3  bnsh.  1}  gall.  Eng. 
1  simmer=6  5-16  galls.  Eng. 
FOR  LIQUORS. — 1  ohm  a  80  maas  a  4  schoppen. 
1  maas=l  gescheid=3  5-32  pints  Eng. 
1  ohm =31  5-16  galls. 
1  fuder=6  ohms;  1  stuck =8  ohm. 

GERMANY. 

Thrre  can  be  properly  no  classification  under  thig 
general  head.  See  Frankfort  on  the  Main,  which 
is  the  principal  commercial  town  of  Germany. 

GREECE. 

(Principal  Commercial  Cities,  ATHENS,  NAUPLIA, 

ETC.) 
Money. 

clrarhm.  lept.  £    s.  d.        $  c.  m. 

23        15      ..         ..  =  1    0  0  =  4  840 

1        30      ..         ..  =0    1  0  =  0  242 

0  11      ...         ..  =0    0  1  =  0  020  2-12 
43          Oorgoldpieco  =  1  10  6  =  7  38  1 

5          0  or  silv.  piece   =0    3    9  =  0  90  7  6-12 

1  0      ..         ..       =00    8;=  0  IV  611-24 
1  drachme  is  equal  to  100  leptas. 

HAMBURG  AND  LTJBECK 

(Commercial  Cities  of  GERMAN  Y). 
Money. 

mk.  c.  schil.  pfen.  £    8.    d.      $  c.  m. 

lo  8  0        ..  =100  =  4  84  0 

0  13J  0        . .  =  0    1    0  =  0  24  2 

0  1  8        ..  =001  =  0  02  0  2-12 
8  0  0  or  1  ducat  =093  =  22386-12 
3  0  Oorldol.cur.=  0    4    4  =  10488-12 

1  0  0        ..  =01    2i=  0  29  26-12 
0  1  0         ..  =00    0}=00153-24 

1  mark  current  is  equal  to  16  schillings. 
1  thaler=3  marks =48  schillinge;  but   they  have 
two  different  values. 

1st — According  to  the  coin,  called  current ; 
2d — Imagined,  used  in  trade,  and  called  banco, 
generally  25  per  cent,  better  than  current. 

1  murk  currency  =  $0.26. 
Exchange  on  London,  14  marks  banco,  m.  or  1.,  for 

£1  sterling. 

"      on  Paris,  fr.  1.50   to  fr.  1.70  per  mark 
banco. 


SUPPLEMENT. 


3J9 


Weight. 

1  pound=16£  oz.  avdp.  Engl. 
1  pound=32  loth  a  4  quent 
1  centner=lll  lbs.  =  119i  Ibs.  Engl. 
1  ship  pound =2^  cwts.=20  lies  pound. 
1  lies  pound  for  shipping=14  Ib. 
1      "         "  land  carriage  =16  Ibs. 

1  stone  flax,  "       =20    " 

1      '•      wood,  etc.    "  "       =10    " 

For  jewels  the  weight  is  the  same  as  Berlin. 

Measure. 

HAMBURG.  ENGLISH. 

1  foot  ..          ..         =        11.2S9  in. 

100  commercial  Ibs.      . .         =      106.833  Ibs. 
100  feet  ..          ..         =        94.021  feet. 

100  ells  . .          . .         =        62.681  yds. 

100  viertels  =159-39  imperial  gallons. 

lOOfass          ..         =18-135  imperial  qurs. 

1  last          ..         =11  imperial  qrs. 

1  ship  last  ..  =  3  tons. 

1  foot=f2  zoll=9G  achtelzoll. 
1  Ehineland  foot  in  Hainbro'=12i  in.  Engl. 
1  Hambro'  ell=22|  in.  Eng. 
1  Brabunt  ell  in  Hambro' =2T  in.  Engl. 
1  Hauibro'  mile =4  3-5  Engl.  miles. 

Grain. 
CORN— Is  sold  by  the  last  a  3  -wispel  a  10  scheffel 

a  2  wispel  a  10  scheffel  a  2  lass. 
BAJOJET — Is  sold  by  the  stock  a  3  wispel    a  10 

scheffel  a  3  fass. 

1  fass=l  bush.  3  galls.  4*  rints  Engl. 

1  scheffel=2  bush.  7  gall.  1  pint. 

1  wispel =29  bush. 

1  last=10  quarters  7i,  bush. 

EOLLAin). 

A  part  of  the  Netherlands. 

(Principal  Commercial  OVtVs.AMSTERDAM.  HAAR- 
LEM, THE  II AGUE,  ROTTERDAM,  LEYDEN,  «fcc.) 

Money  (at  par.) 

.guilder,  cts.  £    s.  d.      $  c.  m. 

12         0        ..         ..         =100  =  4840 

0       63        ..         ..         =010  =  0242 

0  5        ..         ..         =001  =  0  02  0  2-12 
10        0  gold  10  fl.  piece  =  016    6  =  3  99  3 

5       55  or  ducat    . .         =  0    9    3  =  2  23  8  6-12 

1  0  or  silver  florin    =0    1    8  =  0  43  34-12 
1  guilder  is  equal  to  100  cents. 

Weights  and  Measures. 
DUTCH.  ENGLISH. 

1  foot        . .         . .         =11  1-7  in. 
lell  ..         ..         =  27 1-12  in. 

1  last  for  corn   . .         =10  qrs.  5£  bush.  Win- 
chester measure. 

1  aam        . .         . .         =41  wine  gallons. 
1  hoed      . .         . .         =5  chaldr.  Newcastle. 
1  last  for  freight  =  4000  Ibs. 

1  last  for  ballast  =  2000  Ibs. 

LOMBA.RDY. 

(Principal  Commercial  Cities,  VENICE  and  MI- 
LAN.) 
Money. 
1  lira  Anstriaca  =  100  centesimi  or  20  soldi  a  5 

centesiini. 
1  lira  Austriaca  =  $0.16  cents. 

The  Austrian  is  the  current  coin,  under  other 
names. 

2  gulden  =  1  scudo  nuovo  =  $0.96. 
1  gulden  =  £  scudo  ntiovo  =  $0.48. 
I  gulden  =  |  scudo  nuovo  =  $0.24. 
1  gulden  =  1  lira  Austriaca  =  $0.16. 


Exchange  on  London,  30  lira  Anstriache  m.  or 
1.  for  £1  sterlg. 

Exchange  on  Paris,  fr.  85.00  m.  or  1.  per  L  Aust. 
100* 

Weight. 

1  libbra=l  kilogramme=2  Ib  Sioz.  avd. 
1  libbra  =10  oncie=100  grossi=looo  denari. 
1  quintale=100  libbre. 
1  rubbo=10  libbre. 

Measure. 

Equal  to  the  French. 
1  metro=10  pal  mi  =  100  diti=100o  adomi. 
1  miglia=1000  metri. 

CORN.— 1  soma=l  hectolitre,  French. 

lsoma=10  mine=lOOpinta=1000  coppi. 

MEXICO  AND  MONTE  VIDEO. 

MEXICO,  Capital  of  Republic  of  Mexico. 

MONTE  VIDEO,  Capital  of  Repi&lic  of  Uraguay 

(or  Banda,  Oriental),  S.  A. 


MEXICO. 


Money. 
£ 


s.  d. 
0 


$  c.  m. 
=  15  73  0 
=    7865 
=    3  93  2  6-12 
=    0  96  8 
=    1  00  8  4-12 
=    0  50  4  2-12 
=    0  25  2  1-12 
=    0  12  6  1-24 


d-->ls.  rea?s. 

Iti      0  or  gold  doubloon   =35 
8      0  or  i  do.        =112 

0  or  i  do.        =0  16 

0  or  1-16    do.  =04 

0  silv.  dol.  (8  reals)  =  04 
4  do.    *  dol.  =02 
2  do.    i  dol.  =01 

1  do.    k  dol.  =00 
1  dollar  is  eqnal  to  S  reals. 

1  peso  a  8  reales  de  plata  a  4  cuartos. 
1  peso=l  dollar  U.  8.  currency. 
The  piaster  or  duros  of  1S33  and  1834  are  about 
6  per  cent,  less  value. 
COIN.— Gold  doblones  a  16  duros. 

i,  i  and  5  do. 

Silver  duros  or  dollars,  i,  i  and  g. 
Reales  and  £  reales. 

MONTE  VIDEO.    Mcnej. 

The  peso  or  dnro  a  8  reales  de  plata  a  100  cen- 
tesimos. 

This  peso  is  not  eqnal  with  the  Spanish  or  Mex» 
ic.'.n,  and  is  generally  called  the  peso  corriente. 

1  peso  corriente  =  $!'.SO,  or  5  pesos  corrientes  = 
4  pesos  duro  (Spanish  silver  dollar). 

Exchange  on  London  =  52  d.  sterling  for  1  peso 
duro. 

Msasure  and  Weight. 

108  varas=100  yards  English. 

For  the  rest,  see  Spam. 

NAPLES. 

(Principal  Commercial  City,  NAPLES,  the  capital.) 

Money, 
ducat,  grani.  •  £   s.  d.        $  c.  m. 


6 
0 
0 
SO 

1 

0 

3 
30 
2, 
0 
0 
120 

piece  of    .  . 
silver  ducat 
or  dollar  .  . 



1 
0 
0 
5 
0 
0 

0 

1 

0 
0 
3 
4 

0 
0 
1 
0 
4 
0 

= 

4  84 
0  24 
002 
24  20 
0  80 
096 

0 
2 
02-12 
0 
68-12 
8 

0      20  piece  of..      =008=0161  4-12 
9      10  piece  of..      =004=0030  8-12 

1  ducat  is  equal  to  100  grani. 
Ducati  di  regno  a  10  carlini  a  10  grani. 
1  ducato=$0.90. 


320 


SUPPLEMENT. 


COIN.— Gold  pieces  of  6,  4  and  2  ducati,  and 
pieces  of  3  ducati  or  1  oncia,  and  pieces  of  2,  5  and 

Silver  pieces  of  12,  10,  6,  &c.  carlini. 
Scudi  of  12  carlini   and  ducati   in  silver  of  10 
carlini. 

Exchange  on  London,  575  grani  per  £1  sterlg. 
Exchange  on  Paris,  22  a  25  grani  per  1  fr. 

Weight 

1  cantaro=100  rotoli  a  83}  oncie. 
1  rotolo=l  Ib.  15  3-7  oz.  avdp. 

The  libbra  for  gold,  silver,  &c.,  has  12  oz. 
860  trappesie,  7200  acini. 

1  libbra=10  oz,  1£  dwts.  troy. 

Measure. 

1  palmo=12  oncie=60  minuti=120  punti. 

1  palmo= 10 10-27  in.  Eng. 

1  canna=8  paliui=2£  yards  Eng. 

CORN.— 1  carro  a  36  tompli  a  24  mass  or  1  to- 
molo  a  2  mezzetti  a  4  quarti  a  8  stoppeli=12  galls 
li  pints  Eng. 

WIN-E.— 1  carro=2  batti=24  bamli=1440  caraffi, 
in  the  country  15S4  carafli. 
1  barile=9;  galls.,  1  caraffo=l  5-22  pints. 

Oil  is  sold  by  the  salma  a  16  staji  a  256  quarti  or 
1536  inisurelle,  and  weighs  about  350  Ibs.  Ens. 

The  salma  of  Bari  about  312  and  of  Gallipoli  only 
295  Ibs.  Eng. 

1  quarto  in  measure =5-6  pint. 
1  staja  in  measure =27  galls. 


THE  NETHERLANDS. 

{Principal  Commercial  City,  AMSTERDAM.) 
Money. 

1  gulden=100  cents=l*.  Sd.  English =$0.40.3  4-12 
5  cents=l  stuiver=lrf.  English =$0.02.0  2-12. 
?iguilders=$1.00. 

COIN.— Gold  pieces  of  10  and  5  gulden.  Silver 
pieces  of  3  and  1  gulden,  50,  25, 10  and  5  cents. 

Old  gold  coin.— Ducats  weighing  52  4-5  grains 
English,  double  ducats,  ryders=14  gulden. 

Butter  is  sold  by  the  ton,  which  differs  from  the 
common  ton=336  pounds  Holl.  1  pound=15-12 
avoirdupois.  1  ship-pound =300  pounds. 

Exchange  on  London,  11  g.  80  cts.,  more  or  less, 
for  £1  sterlg. 

Exchange  on  Paris,  2  fr.  10  cts.,  more  or  less, 
per  gulden. 


Weight. 


lood. 
10 
1 


wl-tj. 
100 
10 

1 


korrels. 
1000 
100 
10 


1  lb.=l  Ib.  1£  oz.  Avdp. 

Measure. 

The  Ell^l  French  metre=391  inches  English. 

roede.        ell.  palm  duim.  streep. 

1      =10      =100      =     1,000      =     10,000 

1      =      10      =       100       =      1,000 

1       =         10       =         100 

1       =  10 

1  myl  (mile) =1,000  ells=|  mile  English. 
FOB  CORN.— 1  mudde=2  bushels  61-  gallons. 
1  mud=10  schepel=100  kop=l,000  maajtes. 
1  last=80  mudden. 

FOR  LTQPORS.— 1  vat=22  1-10  gallons  English. 
1  vat=100  kann=l,000  maatj.= 10,000  vingerh. 


NORWAY. 

(Principal  Commercial  City,  CHRISTIANA.) 

Money. 

sp.  dol.  skil.  £    s.    d.      $  c.    m. 

4  75  ..  ..  =100=4840 
0  28  ..  ..  =010=0  24  2 
0  2i  ..  ..  =  0  0  1  =  0  02  02-T2 

0  24  or  1  mark..         =00    9^=01917-12 

1  0  specie  dollar        =0    4    4=1  01  8  8-12 
0      60  orlrigsbankdol=  0    2    2=05244-12 
0       1  nearly       ..         =00    C*=  0  01  0  1-12 

1  specie  dollar  is  equal  to  120  skillings. 

POLAND. 

(Principal  Commerical  City,  "WARSAW.) 

Money. 

flor.  grosch.  £   s.    d.       $  c.      m. 

42        0         ..  .         =100=4  84  0 

2        3         ...      ..         =010=0  24  2 

0  5         ..         ..         =001=0  02  0  2-12 
18      15  or  1  gold  ducat  =0    9    3=2  23  8  6-12 

8        0  or  1  rix  dollar     =0    4    0=0  96  8 

1  0  or  1  silver  florin  =  0    0    5|=  0  11  5  23-24 

1  florin  is  equal  to  30  groschen. 
Formerly,  the  gulden  a  30  graschm  Polish. 
1  gulden  =  $0.11£  cents. 

At  present  the  Russian   coin  is  the  only  legal 
tender. 

Bank  notes  of  the  Polish  National  Bank  of  5,50 
and  100  guilders. 

Exchange  on  London,  82  Polish  gulden  M.  or  L. 
for  £1  Sterling. 

Exchange  o'n  Paris,  fr.  60.50  a  fr.  60.75  per  100 
gulden. 

Weight. 

1  funt  (lb.)=14  7-16  ounces  avdp. 

1  funt  (lb.)=13.|  ounces  troy. 

1  lb.=16  oz.=32  loth =128  drams  a  3  scruples  a  24 

grains. 

1  centner=3  stones=100  lbs.  =  87  7-8  Ibs.  avdp. 
Wool  is  sold  by  the  stone  of  82  Ibs. 

Measure. 

1  foot  (stopa)=lli  in.  Eng. 
1  ell  (lokiee)=25  in.  Eng. 
1  mile=8  wersts=5  miles  Eng. 
CORN.— 1  kwart=2  litre=l?  pint  Eng. 

1  korzek=128  kwarts=28  gall.  Eng. 

PORTUGAL. 

(Principal  Commercial  City,  LISBON.) 

Money, 
reis.  £    s.    d.    $  c.    m. 

4120        =100  =4  84  0 

206        =0    1    0  =0  24  2 

20orlvintem       ..         =00    1,1=002233-48 
6400  or  gold  Joannose         =1  16    0  =8  71  2 
1 000  silver  crwn.  or  mil  reis=0    4    8  =1  12  94-12 
400  or  crusado          ..         =02    3=05446-12 
1  mil  rcis  is  equal  to  1000  reis. 

Accounts  are  kept  in  rois. 
1  milrei  (or  1000  reis)=2  1-12  new=2£  old  cruza- 

dos=10  testons=25  reales  ;  1  rei=6  ceitis. 
1   conto  de  reis  (1   million    reis) =£270    sterling 
=  $1,296  (the  dollar  at    the  rate  of  50    pence 
English). 

1  milree=$1.25. 
1  crusado  velho=about  $0.50. 
1  crusado  no vo= about  $0.60. 
COIN.— Gold    pieces  of  24  and  12  thousand  reis 
=$16.80  and  $33.60. 


SUPPLEMENT. 


321 


Silver  pieces,  1,  |.  i,  J  cruzado. 

Exchange  on  London,  1  milrei  for  59  pence. 

on  Paris,  fr.  6.2J  a  fr.  6.3J  per  milrei. 

Weight 

1  quintal  a  4  arrobes  a  32  libras  a  2  marcas. 
llibra=llb.  avdp.  Eng. 

GOLD  AND  SILVER. — 1  marco=S  oncas=64  outa- 
va3=4tiOS  grainos. 

1  inarca=i  lb.=8  8-29  oz.  troy. 
1D1  carats  of  jewels  =  1  oz.  Eng.  troy. 


ROME. 

(Capital  of  the  PAPAL  STATES.) 

Money. 

pioli.baj.  £    s.    d.        $  c.    m. 

4ii      0  ..         ..  =1    0    0=  4  84  0 

25  ..         ..  =0    1    0=  0  24  2 

02  ..         ..  =0    0    1=  0  02  02-12 

100    0  gold  10  scudi  piece  =2    2    6=10285 
10    0  silver  scudo    ..         =04    2=10084-12 
10  ..         ..         =0    0    5=  0  10  010-1J 

1  paoli  is  equal  to  10  bajochi. 


Msasure. 

Thepe=12J-  in.  Eng. 

BTJSSIA. 

The  vara=43  4-5  in.  Eng. 
The  covado=26  7-10  in.  Eng. 

(Principal  Commercial  City,  ST.  PETEESBTTRO.) 

The  passo  geometrico=li  vara. 
1  inile=4  miles  Eng. 

Money. 

CORN  is   sold  by  the   moyo  a  15  fanegas  a  4 

rouble,  hop.                                £  s.  d.     $  c.  m. 

alqueiras  a  4  quartos  a  8  selamis. 
1  moyo=23  bushels  Eng. 
1  fanega=ll^  galls.  Eng. 
TVrvE  AXD  OIL.  —  1  tonelada  a  2  pipas  or  botas=52 
almudas=lU4  alquires  or  potes  and  624  canadas. 
1  alrnude  of  Lisbon  =3  galls.  5  pints  Eng. 
1      "         of  Oporto  =5  galls.  5  pints  Eng. 
1  canada=13  1-16  pints  Eng. 

6      33            ..         ..         =100  =  4840 
0      32           .  .         .  .         =  0    1  0  =  0  24  2 
0        21                    ..         =001  =  0  02  02-12 
5      15  gold  half  imper.    =  0  16  3  =  3»93  26-12 
3        0  ducat           ..         =0    92  =  22184-12 
1        0  silver  rouble          =0    3  2  =  0  76  64-12 
1  rouble  is  equal  to  100  kopeks. 
COIN*.  —  Gold  imperials  of  10  and  5  roubles  (silver). 
Silver,  rouble,  and  pieces  of  75,  50,  40,  3  ', 

&c.,  to  5  kopeks  silver. 

PBTJSSIA. 

Bank  notes  from  1  to  1000  roubles  silver. 

(Principal  Commercial  City,  EERLIX.) 

Exchange  on  London,  from  39d.  to  42d.  for  1 
rouble  silver. 

Honey. 

Exchange  on  Paris,  from  fr.  4.10  to  fr.  420  per 

rouble  silver. 

thai.  per.  pf.                             £    s.    d.       $  c.    m. 

6    20    0      ..         ..        =  1    0    0  =  4  84  0 
099..         ..         =010  =  0  24  2 

Weight  and  Measure. 

0      0  10      ..         ..         =  0    0    1  =  0  C2  02-12 

RUSSIA*.                          ENGLISH, 

5    2J    OgoldFrederick=  0  16    9  =  4  05  36-13 

1  arsheeu*            .  .         =28  in. 

100  silver  thaler     =0    3    1  =  0  74  6  2-13 

1  sashent              .  .         =7  feet 

0      1    Osilbergroschen=  0    0    li=00255-24 

100  feet      .  .         .  .        =  114i  ft. 

1  thaler=33  silver  groschcn  a  12  pfenning. 

1  werst      .  .          .        =5  furl.  12  poles. 

11X                                                        —    A3"!  ft  *t  trr« 

COINS.—  Friedrichs  d'or=16*.  6<7.  English  =$3.96. 
Double  do.  33*.  =$7.92.     Half  do.   8*.   3d.  =$1.93. 
In  silver  pieces  of  2,  1,  |,  ±,  £,  1-12  thaler.    Do  of  2, 

10.                 .  .               .            —    Oolo.U  £T"S. 

100  Ibs.       .  .          .        =  90.26  Ibs.  avdp. 
1  pood        .  .          .        =36  Ibs.  1  oz.  11  dr. 
1  chetwert              .         =  5.952  Wine.  bush. 

1,  i  groschen. 

100    do  =  74.4  quarters. 

Bank  notes  of  1,  5,  5\  IfH,  5^0  thaler  freely  taken 
in  the  whole  of  Germany  for  their  nominal  value. 
Wool  is  sold  by  the  stein   of  22  pounds  =22} 

1  wedro     ..         *.         =  3J  wine  gallons. 
More  particularly  — 

pounds  avoirdupois. 
Exchange  on  London,  6  thalers  25  gr.,  more  or 
IP<V<L  for  £1  sterling.     Do.    Paris,   fr.   3.75.    innr«  nr 

Weight. 

1  r»ATiTirl  ffnnt^=14-l  or.  ftvdn. 

less,  per  tnaler. 


1  pound =467 


Weight 
'•10  grammes  French=l  1-52  pound 


avoirdupois. 

1  cwt.  =  110  pounds  Pr.=113  7-1G  Ibs.  avoirdupois. 
1  last  (shipping)  is  4,000  pounds. 

Gold  and  silver  are  sold  by  the  mark=^  pound 
=7  oz.  10\  dwts.  troy  English. 

The  mark  is=233  grains. 

For  assay  of  silver  the  mark  is  divided  into  16 
loth  a  13  grs. ;  and  of  gold  into  24  carats  a  12  grs 
1  carat  of  jewels  is=9-160  quent=l  dwt.  7  5-7 
grains  troy. 

Measure. 

The  foot=12',  inches  English. 

1  ruthe  =  12  feet=144  zoll  =  1723  linien. 

1  ell  =254  zoli=26i  inches  English. 

1  faden=6  feet.    1  mile=4  2-5  miles  English. 

FOR  CORN.— 1  schefiel=H  bushel. 

1  scheffel=16  metz  ;  24  scheffel=l  wispeL 


1  pood=40  lb.=36i  Ibs.  avdp. 
1  bercowitz=10  poods =362^  Ibs.  avdp. 
1  bruttolast=6  chetwerts. 
(The  funt  is=95  solotnick.    1  sol.=96  doll.) 

Measure. 

1  foot          =1  foot  Enrr. 

1  arsheen    =  28  in.  Eng. 

1  sashen      =  3  arsheens. 
1   sashen=3  arsheens=7  feet=43  worschecks=84 

inches=1008  lines. 
1  werst=500  sashen=f  mile  Eng. 

CORN;  &c. — 1  chotwert=4  pajok. 
8  tschetwerick=32  tschewerka=64  garner. 
1  chetwert=5  bushels.  6  galls.,  2  pints,  Eng. 
1  tschetwerick=57-9  sails.  Ens. 
1  kuhl  or  sark=10  tschetwericki. 
1  wedro =2 1  galls.  Eng. 
1  fass=40  wedroja. 


21 


*  1  arsheen=28  in.  Eng. 
t  1  sashen =3  arsheens. 


322 


S  tJP  PL  EM  E  NT. 


SARDINIA. 

(Principal  Commercial  Cities,  GENOA  and  TURIN.) 

Money. 
The  lira  nuova=l  franc  a  100  centesimi=9i<?.  Eng. 


COIN.—  Gold:  Pieces  a  20,  40,  80,  and  100  lire 
nuove  or  $3.75,  $7.50,  $15.00,  and  $18.75.  Silver 
scudi  d'argento  a  5  lire  nuove.  Pieces  of  2  and  1 
lire  and  51)  and  25  centesimi. 

Bank  notes  of  5,  10,  and  20  scudi. 

Exchange  on  London,  25.50  lire,  more  or  less,  for 
£1  sterlg. 

Exchange  on  Paris,  21  lire  per  fr.  20. 

Weight 

IN  GENOA.    1  peso  grosso=121-6  oz.  avdp. 

1  peso  sottile=l  Ib.  dwt.  18  gr.  troy. 
IX  TURIN.    1  libbra=13  oz.  avdp. 

The  Custolns  use  the  French  kilogramme. 
'Gold  and  silver  weight  is  the  marco=8  uneio  a  24 
denari  a  24  grani. 

1  rnarco=S  oz.  troy. 

Measure. 
IN  GENOA.    1  palmo=9J  in.  Eng. 

FOB  CORN—  1  inina=8  bush.  2i  gall.  Eng. 

1  mina=8  quarti=96  gombette, 
FOB  WISE—  1  barile=16£  galls.  Eng. 

1  mezzarola=2  barili  =  100  pinte. 
FOR  OIL—  1  barile  =  14J-  galls.  Eng. 
IN  TURIN.    1  piede  liprando=l  foot  8*  in.  Eng. 
1  picde  manelle=12r  in.  Eng. 
1  r^y  (ell)=23i  in.  Eng. 
FOB  COEX  —  1  sacco=5  emine  a  8  copi  a  24  cuc- 

chiari. 

1  sacco=25i;  galls.  Eng. 
FOB  WINE—  1  brenta-10  4-5  galls. 

1  carro=10  brenta,  a  86  pinte  a  2  boc- 
cali. 

SAXONY. 

(Principal  Commercial  Cities,  DUESDEN  and 
LEIPSIC.) 

Money. 

rd.  gn.  pf.  £    s.   d.       $  c.  m. 

6150        ..         ..         =100=4840 
099        ..         ..        =010=0  24  2 

0  0  10        ..         ..         =001    =00202-12 
5  12^  0  or  Augnst.-d'or  =  0  16    2   =  3  91  2  4-12 

1  10    0  or  specie  thaler  =  0    311    =  0  94  7  10-12 
1    0    0  currency  ..        =  0    8    1    =  0  74  62-12 
010        .          ..        =  0    0    1J=  0  02  OC-'i4 

1  thaler  a  80  groschen  a  10  pfenninge. 

1  thaler  =  2s.  llrf.  Eng.  =  $0.70.5  10-12. 

COIN.—  August  d'or=16*.  Eng.  =  $3.87.2. 

Silver  pieces  of  2,  1,  £,  1-6,  and  1-12  thaler. 
Paper  money  is  issued  by  the  Government  in  notes 

of  10,  5,  and  1  thaler. 
By  the  Bank  of  Leipsic  in  cotes  of  20,  100,  200,  500, 

and  1000  thalers. 

Also  1  thaler  notes  by  the  Leipsic  Dresden  Railway 
Company. 

Exchange  on  London,  6  thaler  25  groschen,  more 
or  less,  per  £1. 
Exchange  on  Paris,  fr.  8.50  a  fr.  8.75  per  thaler, 

Weight 

llb.=llb.  l^oz.  avdp.  Eng. 
1  cwt.=100  lbs.=1000  millas. 
For  the  retail  trade  the  Ib.  ia  divided  into  82  loths, 
a  4  quenta. 


Measure. 

1  foot=ll£  in.  Ens. 
1  ell  =3-5  French  metre =24  in.  Eng. 
FOB   CORN— 1  schaffel  =  100  litres  French  =  22 
galls,  nearly. 

12  schaffels=lmalter,  2  malters=l  wispel. 

1  wispel  =  66  bushels  Eng. 

FOB  LIQUIDS — 1  oxhooft=l|  ohm=3  eimer=210 
kanns. 

1  fuder=4  oxhoofts. 

1  kanue=l  litre=l|  pints  Eng. 

EMTSNA  AND  THE  LEVANT. 
Money. 

Like  Constantinople.  In  the  Levant  are  like- 
wise used  to  a  great  extent,  Spanish  dollars  and 
Dutch,  Hungarian  and  Venetian  ducats.  Likewise 
German  Conventions  thaler =$0.96  to  $1.00,  bein:j 
subject  to  variation. 

Exchange  on  London,  1C5  piasters,  more  or  less, 
for  £1. 

Exchange  on  Paris,  fr.  4.75  to  fr.  5  per  piaster. 

Weight 

1  cantaro=7|  battman=22£  chequis=45  okes=100 
rotoli  a  18J  drachms. 

The  oka,  as  a  gold  and  silver  weight,  has  400 
drachms,  and  is  equal  to  3|  Ibs.  Troy. 
1  cantaro  =  127|  Ibs.  Troy. 
1  rotolo      =  1  Ib.  4|  oz. 

Goat's  hair  is  sold  by  the  chequi  a  800  drachmas. 
Silk  is  sold  by  the  teffei  a  610  drachmas. 
Opium  is  sold  by  the  teffei  a  250  drachmas. 
1  drachm =49  3-5  grains  troy  weight. 

Measure. 

1  pik  =  27  in.  Eng. 
COEN.— The  killo\v=llf  gall.  Eng. 

SPAIN. 

(Principal  Commercial  City,  MADRID.) 

Money. 

dols.rls.  £   s.   d.       $  c.  m. 

4      14  barley         ..         =1    0    0  =  4  84  0 

0  5          .'.         ..         =0    1    0  =  0  24  2 
16        0  or  gohl  doubloon=3    6    0=15972 

4        0  or  gold  pistole      =016    6  =  3  99  3 

1  0  or  silver  dollar    =0    4    8  =  1  02  8    6-12 
0        1  or  real  vellon       -0    0    2jj=  0  05  3  45-48 

\  dollar  is  equal  to  twenty  re:ils. 

They  use  eight  different  sorts  of  money : — 1. 
Castilian.  2.  Mexican.  3.  Catalonian.  4.  Ma- 
jorcan.  5.  Valencian.  6.  Arragon.  7.  Navarre, 
and  8.  The  Canarian  money. 

The  Castilian  is  the  chief,  and  is  1  real  de  plate 
antigua=l  15-17  real  de  vellon=16  cuartos=34 
maravedis  de  plata  antigua=64  marav.  de  vellon 
=640  Castil.  dineros. 

10|  reales  de  plata  antigna=l  piaster. 

1  piaster  or  duro=4s.  4d.  Enff.  =  $1.04  8  8-12. 

1  real  de  plata =5d.  Eng.  =  $0.10.0  10-12. 

COIN. — Gold,  1  quadrupel  pistole=8  eseudos= 
$16  to  $15.60=doblon  or  onza  de  Oro=$16  subdi- 
vided into  |,  },  f,  and  1-16.  Peso  duro  or  dollar 
need  not  be  described. 

Exchange  on  London,  4fld.  sterling,  more  or  less, 
per  peso  de  plata  antigua=48d.  to  52d.  Eag.  per 
dollar. 

Exchange  on  Paris,  fr.  5.10  a  fr.  5.30  per  peso  duro. 

Weights  and  Measures. 
SPANISH.  ENGLISH. 

1  cana  =  21  inch,  nearly. 

100    "  =  58.514  yards. 

100  qnarteras  =  23.536  Win.  qrs- 

100  Ibs.  =  88.215  Ibs.  avdp. 
More  particularly — 


SUPPLE  ME  XT. 


323 


Weight. 

1  Castilian  marca=S  1-7  oz.  avdp.  or  7  oz.  3  4-25 

dwts.  troy,  Eng. 

1  marca=8"onzas=64  octaves  =46r>8  granos. 
1  quintal  uiacho=6  arrobas=150  libras. 
800  marcas  =  152±  Ibs.  avdp. 
1  quintal=4  arrobas=100  libras=101£  Ibs.  avdp. 

Jewels  and  pearls  are  weighed  by  the  CasUlian 

ounce  a  14  )  quilates,  a  4  granos. 
1  oz.=43H  grains  troy. 


1  pie  =11  }  in.  Eng. 
1  estado=2  varas=6  pies=5  ft.  6^  in.  Eng. 
1  league  =4J  miles  Eng. 
FOR  CORN.  —  1  cahir=12  fanegasa!2  celeminesor 

almudos  a  4  quartillos. 
1  fanega=12j-  galls.  Eng. 
FOR  LIQUIDS.  —  1  cantaroorarrobamayor=Sazum- 

bres=32  quartillos. 
1  arrobamayor=3  galls.  3}  pints  Ens:. 
1  arrobamenor  for  oil=2  galls.  5J  pints  Eng. 
1  moyo=16  cantaros.    1  pipa=27  canturos. 
1  bota=3J  caataros. 

SWEDEN. 

(Principal  Commercial  City,  STOCKHOLM.) 

Money. 

rd.  skil.  £    s.  d.  $  c.  m. 

12    0   in  banco  ..       =10    0=4840 

0  23  ..  ..=01    0=0  24  2 
02}          ..  ..=00    1=0  (12  0  2-12 
5  25   or  1  gold  ducat..       =09    2=2  21  8  4-12 
2  25    or  1  specie  silver       =04    4=1  04  8  8-12 

1  0   banco       ..         ..       =01    8=04034-12 
1  12*  or  half  specie  silver  =  02    2=0  52  4  4-12 
1  rd.  banco  is  equal  to  43  skillin<rs. 

1  silver  species  is  equal  to  96  skillings. 
1  riksdaler  specie  a  43  skillings=$1.05. 
Payments  are  however  made  chiefly   in   bank 
notes  of  8,  10,  12,  14,  and  16  skillings,  and  2,  3,  5,  6, 
9,  up  to  53  riksdalers. 

Banco=l  riksdaler  specie. 

Exchange  on  London,  12  dalers  banco  for  £1  sterlir. 
Exchange  on  Paris,  fr.  2.10  to  fr.  2.15  for  1  riksdal. 

Weight. 

1  skal  pound.         =    15  oz.  avdp. 

1  schip  pound        =  4M)  skal  Ibs. 

Icwt.  =12)  Ibs. 

1  scale  of  spelter  =  165  Ibs. 

1  stone  wool          =    32  Ibs. 

1  mark  (for  gold)  =      6  oz.  10  dwt  troy. 

Measure. 

1  foot  =1  foot  Eng. 
1  faam=3  alnar=6  feet=17  rerthum. 
1  alnar=2  feet  Eng. 
CORN.—  1  tonn=4  bush.  Eng. 
1  toun=8  quarts=32  kappar=56  cans=44S  quarr- 
tiera, 

WINE.—  2  pipes=l  fuder=4  oxhoofte=12  eimer 
=  7iJ  stop. 

SWITZERLAND. 

(Principal  Commercial  Cities,  GENEVA, 

BERN,  BASLE.) 
Money.    Old  System. 

fr.  batz.  rap.  £   s.    d.          $  c.  m. 

17    7      5  ..       =100     =    4840 

087  ..       =010     =     0  24  2 

007  ..       =001     =    0  02  0    2-12 

4  0  0  piece  of  =  048  =  1129  4-12 
10  0  or  10  batz  =  0  1  1|  =  0  27  2  3-12 
01  0  ..  =001£=002G  32-36 

1  franc  is  equal  to  10  batzen. 


New  System— as  in  Franca 

1  frane=10  batzen  a  10  rappen  or  1  livre  a  20  sols  a 
12  deniers. 

1  franc=l  livre=$0.27. 
COIN.— Gold  pistoles  a  32  francs ^$3.63. 

les  a  16  francs- $432i. 


Silver  pieces  of  40,  20,  10.  and  5  batzen. 
|      N.  B.— Each  Canton  has  besides  these  its  own 
currency. 

Exchange  of  Basle  on  London,  17  francs  5  rappes, 
more  or  less,  for  £1  sterling. 

Exchange  on  Paris,  fr.  1.50  per  fr.  1,  or  50  per  cent, 
premium,  more  or  less,  in  favor  of  liasie. 

Waight 
1  cwt.=100  lbs.=50  kilogr amines =110i  Ibs.  avdp. 

Eng. 
1  lb.=^  kilogramme=l  Ib.  If  oz  avdp.  Eng. 

Measure. 

The  basis  is  the  Helvetian  foot. 

1  foot=3-10  French  meter=ll  17-20  in.  Eng. 

2  feet=l  ell ;  4  feet=l  stab  or  staff. 
16,000  feet=l  hour  (mile)=3  Eng.  mil- •<. 

FOB  CORN.— 1  malter=10  viertel^l"    :-:ur. 
1  malter=4  bushels  1  j;a:i.  Eng 
1  immir=3|  pints. 

WINE. — 1  ohm    =100  inaas  (or  measures). 
1  ohm    =33  galls.  Eng. 
1  maas  =3$  pints  Eng. 

TURKEY. 

(Principal  Commercial  City,  CONSTANTINOPLE.) 

Money. 

pias.  par.  £  s.    d.     $  c.  m. 

109      0  ..  =1    0    0  =4  84  0 


5?-    0 
0    13 


0  =0  24  2 

1  =0  02  0  2-12 
0  =7  50  2 

0  =3  35  6 
2J=0  04  5  9-24 

2  =1  00  8  4-12 


200      0  gold  new  dble.  seq.  =111 
100      0    "    1  seq.  =0  18 

10  ..  =00 

22      0  or  1  Spanish  dollar  =0    4 
Piaster  a  40  paras  a  3  aspers. 
Also  piaster  (grush)  a  100  aspers. 

1  piaster=2irf.  English =$0.05. 
1  purse  silver  is  500  piasters. 
1  purse  gold  is  30,000  piasters. 
1  juk  is  100,000  coined  aspers. 

The  government  or  bank  notes  bear  8  per  cent, 
interest. 

Exchange  on  London,  104  piasters,  more  or  less, 
for  £1  sterling. 

Exchange  on  Paris,  from  400  to  410  piasters  for 
100  francs. 

Weight. 

1  pound,  chequi=llj  oz.  avo:rdupois. 

1  oka=2  Ibs.  12  oz.  avoirdupois. 

1  oka =4  chequi=400  drachmas. 

1  taffee=610  drachmas. 

1  batman =6  okas. 

1  cantaro=44  a  45  okas. 
Gold  and  silver  weight  like  Alexandria. 

1  chequi  opium =250  drachmas. 

1  chequi  goat-hair=800  drachmas. 
PIECE  GOODS. — 1  mazzee=50  pieces. 

Measure. 

The  large  pikhalebi,archim=27  9-10  inche?  Eng. 

The  small  pik  andassa=27  1-16  inches  Enelish. 
FOR  CORN.-  The  killow=7|  gallons  English. 

1  fortin=4  killows=30  gallons  English. 

1  killow  of  rice  should  weigh  10  okas. 
FOR  LIQUORS. — 1  almud=l  2-5  gallon  English. 

1  almud  of  oil  should  weigh  22  5-S  pounds  avoir- 
dupois. 


324 


SUPPLEMENT. 


TUSCANY. 

(Principal  Commercial  Cities,  FLOBBNCB   and 
LBGHOBN.) 

Money. 

1  lira  Toscana=100  centesimi=7  4-5cL  Eng.= 
$0.15  3-5. 

1  lira  Toscaua=20  soldi=240  denari. 

25  lire  Toscane=21  francs. 

COIN.— Gold:  Kusponi  a  3  zecchini  =  $6  25 

Zecchini  gigliati,  =  2  05 

Half  "  =  1  03 

Silver :  Francesconi  a  Leopoldinl  =  0  96 

Half  "  =  0  48 

Tallari  =  0  92 

Testoni  =  0  80 
Lire  a  12  crazie,  about  15 

Exchange  on  London,  30  lire,  m.  or  1.,  per  £1. 
Paris,  80  to  85  centimes  per  lira. 

Weights  and  Measures. 


LEGHORN. 

1  braccio 
155  bracci 

1  sacco 

4  sacci 
100  Ibs. 

1  centinajo 

1  rottolo 


ENGLISH. 

=  22.93  in. 

r=  100  yards. 

=      2.0739  Winchester  bushels. 
=      1  imperial  quarter  nearly. 

=  74.864  Ibs.  avoirdupois. 

=  100  Ibs. 
=      3  Ibs. 


More  particularly— 


Weight 

1  quintal =100  Ibs.  =1200  uncie  a  24  denari 
1  Ib.  =  12  oz.  avoirdupois. 
1  quintal=74&  Ibs.  avoirdupois. 
FOE    GOLD.— 1  Ib.  =  10  11-12  oz.  troy,  and  Is 
divided  into  24  carati  a  8  ottavi. 
FOR  SILVER,  into  12  uncie  a  24  denari. 
Jewels  are  weighed  by  the  carat  a  4  grant 

Measure. 

1  braccio     =    23  in.  English 
1  mile          =      1  mile,  48  yards,  English. 
The  braccio  used  by  builders=21  3-5  in.  English. 
FOB  CORN. — 1  sacco=3  Btaja=6  mines; 

100  sacchi=201  bushels. 

FOR  WINE— 1  barile=20  fiaschi=80  mezzette= 
160  quartuzzi  =  10  1-30  galls.  Eng. 
1  barile  of  oil=7f  galls  English. 

SHIPPING    MEASUREMENT. 
FOB  GRAIN. — 42  cubic  feet=l  ton  shipping  meas- 
urement. 

1  bushel     =         60  Ibs. 
1  bushel     =      2218|  cubic  inches. 
8  bushels    =  1  quarter. 

1  quarter    =    17745  cub.  in.  or  10.27  ft. 
Therefore  1  ton  will  take  4  quarters  and  one -tenth 
1  bushel  being  equal  to  60  Ibs., 
1  quarter  will  be  equal  to  480  Ibs., 
1  ton=1968  Ibs.  or  17  cwt.  2  qrs.  0  Ibs.  fully. 
1  ship  of  200  tons  measurement  can  therefore 
carry  820  quarters,  but  it  generally  can  carry  much 
more. 


MISCELLANEOUS  TABLE 


FOREIGN  WEIGHTS   AND   MEASURES. 


Arroba  of  Bnenos  Ayres  ..  = 
Amir,  or  Emir,  of  Stuttgard  . .  = 
Balsam  Copaiva,  8  Ibs.  . .  = 

Butt  of  wine        = 

Canado  of  Balsam  Copaiva      ..       = 

Chaldron  coal,  British  Provinces    = 

do.      do.    Cumberland    ..       = 

Cheki  of  opium  (from  Smyrna)       = 

Coal,  a  railway  wason  load,  Pictou  = 

Flax,  head  of,  about         . .     . .       ; 

Foot,  100  feet  St.  Domingo     . .       = 

Honey,  1  gallon  . .        . .      = 

Linseed,  one  bushel      . .         . .       = 

Mudd,  or  maud,  of  Rotterdam        : 

Moyo  of  salt  (Spain)      ..         ..       : 

Modius  of  salt  (from  Ivica,  Spain): 

do.        do.    (Oporto  &  St.  Ubes): 

Mass  (of  Antwerp)  ith  of  ohm        : 

Ohm  do.  ..         ..       ; 

Pou  nds  of  A  ustria,        . .     100  Ibs.  : 

do.        Antwerp,       ..        do.     : 

do.       Bavaria,        ..       do.    - 


25-36  Ibs.  U.  S.     Pounds  of  Beldum. 

100  Ibs.  =103  35-1-00 

78  gallons. 

do.        Brussels, 

do. 

=10835-100 

1        do. 

do.        Bremen, 

do. 

=109  80-100 

130    do. 

do.        Berlin, 

do. 

=103  11-100 

30  pounds. 

do.        Hamburg, 

do. 

=106  80-100 

36  bushels. 

do.        Malaga, 

do. 

=101  44-100 

53      do. 

do.        Netherlands,  .  . 

do. 

=108  98-100 

If  pound. 

do.        Portugal, 

do. 

=101  19-100 

62  cwt. 

do.        Prussia, 

do. 

=103  11-100 

6|-pounds. 

do.        Eotterdam,    .  . 

do. 

=108  93-100 

106  60-100  feet. 

do.       Spain, 

do. 

=101  44-100 

12  pounds. 
47      do. 

do.        St.  Domingo,  .  . 
do.        Trieste, 

do. 
do. 

=107  93-100 
=123  60-100 

143    do. 

do.        Vienna, 

do. 

=123  60-100 

70  bushels. 

Palm  of  Italy,  of  marble 

=  6  inches. 

40      do. 

Quintal  of  France 

=220  54  -100  Ibs. 

23      do. 

10  gallons. 

Skippond  of  Gottenburg 
do.         Gefle 

=300  pounds. 
=314  1-10  Ibs. 

40      do. 

Salt,  one  barrel 

=5|  bushels. 

:  123  60-1  00 

Vara,  Spanish 

=8  feet 

103  35-100 

Yara  of  Baracoa  .  .        .  . 

=20  feet. 

123 

SUPPLEMENT. 


325 


RATES  OF  FOREIGN  MONEY  OR  CURRENCY,  FIXED  BY  LAW. 


The  following  condensed  presentation  of  the  United  States  value  of  Foreign  Currencies,  "Weights  and 
Measures,  is  to  a  considerable  extent  a  repetition  of  what  may  be  found  in  the  foregoing  Tables.  It  is 
here  thus  given,  first,  for  the  greater  convenience  of  this  condensed  form;  and  secondly,  as  giving  the 
specific  values  established  by  law  in  the  United  States,  while  that  presented  in  the  foregoing  is  the  one 
recognized  in  London,  estimated  in  Sterling  Currency,  and  that  reduced  to  Federal  Currency,  putting 
the  pound  at  $t.Si.  The  slight  discrepancies  between  the  two  are  thus  accounted  for,  and  the  reader  will 
hear  in  mind  that  the  following  are  the  popular  values  or  rates  at  which  these  foreign  coins  pass  in  the  U.  S. 

The  Editor  acknowledges  his  essential  indebtedness  for  these  to  a  volume,  entitled  "  United  States 
Tariff,"  &c.,  published  by'Messrs.  Rich  &  Loutrel,  New  York,  to  whose  courtesy  we  are  indebted  for  the 
use  of  these  Tables.  In  it  may  be  found  a  great  amount  of  valuable  information  to  commercial  men, 
respecting  the  Rates  of  Duties  on  foreign  merchandise  and  other  matters.  The  volume  is  compiled  by  E. 
D.  O^  len~  Esq.,  Entry  Clerk  i*i  the  New  York  Custom  House,  and  is  made  the  text  book  in  all  the  Cus- 
tom Houses  throughout  the  United  States  and  by  the  Departments  at  Washington. 


$  eta. 

8) 

136-10 
40 
4} 


Ducat  of  Naples,     ..          

Franc  of  France  and  Belgium, 

Florin  of  the  Netherlan  is, 

Florin  of  the  Southern  States  of  Germany, 

Florin  of  Austria  and  Trieste, 4?* 

Florin  of  Nuremburg  and  Frankfort,    ..         ..  4) 

Florin  of  Bohemia, 43* 

Guilder  of  Netherlands,  &c. — same  as  Florins. 

Lira  of  the  Lombardo  and  Venetian  Kingdom,  1") 

Livre  of  Leghorn, 15 

Lira  of  Tuscany, 15 

Lira  of  Sardinia, 136-10 

Livre  of  Genoa,        136-10 

Milrea  of  Portusral, 113 

Milrea  of  Ma  leira, 103 

Milrea  of  Azores 8-3} 

Marc  Banco  of  Hamburg, 35 

Ounce  of  Sicily,        240 

Pouni  sterling  of  Great  Britain,            ..         ..  4^4 

Pound  sterling  of  Jamaica,          484 

Poun  1  sterling  of  British  Prov.  of  Nova  Scotia, 

New  Brunswick,  Newfoundland  and  Canada,  4  00 

Payola  of  In  lia, 184 

Real  vellon  of  Spain,          5 

Real  plate  of  Spun,            ..         ..         ..         ..  10 

Rupee  Company  and  British  In  lia,      ..         ..  44* 

Eix  dollar   (or    thaler)    of   Prussia    and  the 

Northern  States  of  Germany €9 

Rix  dollar  (or  thaler)  of  Bremen,          ..         ..  73| 
Eix  dollar  (or  thale  -)  of  Berlin,  Saxony  &  Leipsic,   69 

Rouble,  silver,  of  R.issia, 75 

Specie  dollar  of  Denm  irk,            105 

Specie  dollar  of  Norway, 1  06 

Specie  dollar  of  Sweden,  ..         106 

TaleofC.iini 1  43 

Banco  rix  dollar  of  Sweden  and  Norway,       ..  39} 

Bano  rix  dollar  of  Denmark,     ..         .".         ..  53 


Curacoag-jilder, 
Leghorn  dollar  or  pezzo,   . 
Livre  of  Catalonia,  .. 
Livre  of  Neufchatel, 
Swiss  livre,    .. 
Scudi  of  Malta, 
Scudi,  Roman, 
St.  Gall  guilder, 



40 
90  76-100 

:    P 

40 
99  a  99* 
40  36-100 

Rix  dollar  of  Batavia, 
Eoman  dollar, 



75 
.     1  05 

Rouble,  paper,  of  Russia,  . . 

Turkish  piastre, 
Current  mark, 
Florin  of  Prussia,     .. 
Florin  of  Basle, 

Genoa  livre, 

Livre  tournois  of  France,  . . 


21 
18* 


100  grani 
100  centimes 
100       do. 

60  kreutzera 

60       do. 

60        do. 

60        do. 

100  centisimi 

20  soldi 

2U  soldi 
4  reali 

20  soldi 
1000  reas 
1000  do. 
1000  do. 

16  shillings 

SOtari 

20  shillings 


20       do. 
36  fanams 
34  maravedis 
84        do. 
16  annas 

80  groschen 
72  grotes 
80  groschen 
10)  kopecks 

6  marks 

6    do. 
43skillings 
10  mace 


20  soldi 
2)  stivers 
20  sol.-li 
20  sueldos 
20  sols 
100  centimes 
12  tair 

60  krentzers 

43  stivers 


of 


4  pfennings 
4        do. 
4        do. 
4       do. 

100  millesemi 
12  -lenari 
12  denari 
20  soldi 
12 'denari 


12  pfennings 
20  grani 
12  pence 


12    do. 
43jittas 


12  pice 

12  pfennings 

5  swares 

12  pfennings 

16skillings 
16     do. 
12  'ore 
100  candarem* 


12  denari 
12  pfennings 
12  denari 
12  dineros 
12  deniers 

20  grani 
4  pfennings 


f  Varies  from  4  roubles 

i  n<\  v         v       J     65  copecks  to  4  rou- 
100  kopecks     j      b]es  £j  Ck8  to 

[     the  dollar. 
100  aspers 


SUPPLEME  NT. 


A  TABLE  OF  FOREIGN  WEIGHTS  AND  MEASURES, 

EEDUCED  TO  THE  STANDARD  OF  THE  UNITED   STATES,  AND  AS  RECEIVED  AT  THE 
UNITED  STATES  CUSTOM  HOUSES. 

ALEXANDRIA  (Egypt). 

Cantaro  of  100  rottoli  farlbro 

of  15  oz.  (avoirdupois)  . .     =  9"4  Ibs. 

300  rottoli  zaydino  of  2Hoz.  =  18o|   " 

100      "      zauraof83oz.  ..     =  2 '7      " 

100      "      minaof 26}  oz...     =  167     " 
1  oke  400  drams  of  16  carats 

each  .     =  43     " 


Stone  of  flax. . 
Stone  of  wool 
Lispund 

100  Ibs. 


=  20   Ibs. 

=  10     " 

=  14     " 

=  1C9.8  " 


ALICANT  (Spain). 


CADIZ  (Spain). 

Quintal  of  4  arrobas  ..     =     ICO  Ibs. 

1  lb.,  2  marcs,  16  oz.,  or  256 

adarins. 
100  Ibs.  .     =     101.43  Ibs. 


Arroba          =      27   Ibs.  6  oz. 
Quintal         =    109J  Ibs. 

CAIRO  (E^ypt). 
Cantaro,  100  rottoli.  .         .  .     =      93  Ibs. 

AHSTERDAH. 
100  Ibs.  1  centner    .  .         .  .     =     10S.<T,  Ibs. 

1  rottoli         =144  drams. 
r»n«<i                                                J  ^OO  drams,  or 
ucca    —  -j      26.39  Ibs. 

Last  of  grain  =       85.25  bush. 

86  occas         .  .         .  .                =        1  cantaro. 

Ahmofwine           ..         ..     =      41.00  gall. 

Amsterdam  foot      .  .         .  .     =        0.93  foot. 

cinxTA, 

Antwerp  foot           .  .         .  .     =        0.94    " 

Tail                          .          .       —        1\oz 

Rhinlandfoot          .'.'         '.'.     =        1.03    " 

16  tails  =1  catty      ..         ..     =        l.llb. 

Amsterdam  ell        ..         ..     =        2.26  feet. 

100catties=l  picul            ..     =     133  i  Ibs. 

Ell  of  the  Hague     .  .         .  .     =        2.28    " 

Ell  of  Brabant         ..         ..     =        2.30    « 

CONSTANTINOPLE. 

Medden  or  measure  of  coal    =        2$  bush. 

Quintal          =     IPO  rottolis. 

do.              .  .         .  .         .  .     =      45  okes. 

ANCONA  (Italy). 

do.               =     176  cheques. 

100  Ibs.  Roman        .  .         .  .     =    102.75  Ancona. 

do.              =127  Ibs. 

100    "    Ancona                 .  .     =      73.75  Ibs. 

One  oko         =  -j      2  JJ*?'  13    oz>    ~ 

ARRAGON  (Spain). 

CALCUTTA. 

Libras  of  100  Ibs  =      77.01  Ibs. 

Maund           =      40  seers. 

Quintal,  4  arrobas  of  36  Ibs.    =     112.00    " 
BA330RA.  (Persian  Gulf). 

Seer     =       16  chattacks. 
English  factory  maund     .  .     =       74  Ibs.  10  oz. 
Seer     =        1  lb.  13  oz. 

Maund  attary,  25  vakias  tary  =      23.05  Ibs. 

Chattack        =        1  oz. 

One  vakia      =      19  oz. 

BATAVIA  (E.  Indies). 

Bengal  bezar  maund  is  10  per 
cent,  heavier  than  the  fac- 
tory maund. 

Large  bahar  .          .  .         .  .     =        4£  peculs. 

Small      "       =        8 

ijczar  maunu           .  .         .  .         •<             drains 

1  pecul          .          .  .         .  .     =    100  catties. 

Seer     =        2  Ibs.  1  3  |  drams. 

1  catty           =       16  tales. 

Chattack       =        2  oz.  5-6  drams. 

1  pecul          =135  Ibs.  10  oz. 

IEH~I!T  (ZTorway). 
Bhippond  of  20  lisnonds    ..     =    820  Ibs. 
Centner  of  6^  lispomls      ..     =     100    " 
Lispond         =      16    " 
Waag.  8  bismar  Ibs.           ..     =      8G   " 
1  lb.,  2  marcs,  1G  oz.,  32  loths. 
100  Norway  Ibs  =     110.23  Ibs. 

DENMARK. 

100  Ibs.  =1  centner  ..         ..     =    110.23  Ibs. 
Barrel  or  toende  of  corn  ..     =        3.95  bush. 
Viertel  of  wine        ..         .  .     =        2.04  galls. 
Copenhagen,  or  Rhineland  ft.=        1.08  foot. 
Centner  or  100  Ibs.  Denmark  =     110.28  lb. 
Shipfund=20  lispunds       ..     =    820  Ibs. 
1  lispund        =      16    " 

CHRISTIANA  (ITorway). 
Shippond      =    352  Ibs. 

1  bismerpund           .  .         .  .     =      12    " 
1  waag=3  bismerpunds    .  .     =      86   " 

LAURWIQ  a:orx7a7). 

ENGLAND. 

Bhippond      =    852  Ibs. 

Old  ale  gallon          ..         ..     =        1.22  galls. 

BOMBAY. 

Imperial  gallon       .  .         .  .     =        1.20     " 
Old  wine     "            ..         ..     =        1.00     " 

Ccindv..                               .     =    26^  Ibs. 

Quarter  of  grain,  or  8  imperial 

Maurid          =      28    " 

bushels       =        8.25  bush. 

Beer    *=      lll-5oz. 

Imperial  corn  bushel,  or  8  im- 

Candy         =      20  maunds. 

perial  gallons       .  .         .  .     =        1.03     " 

Maund           =      4  )  seers. 

Old  Winchester  bushel     ..     =        l.CO     " 

Beer    =      3J  pice. 

Imperial  yard          ..         ..     =      36  inches. 

rp                 ,                                    (  144-  175th  sofa  Ih, 

BBhEXESt 

Troy  pound  =  -J         nvoirdnpoi8. 

Shlpfund       =        2J  centners. 

Newcastle  chaldron          .  .     =      86  bushels. 

Centner         =116   Ibs. 

Stone  =      16  Ibs. 

VTaagofiron  =    120     " 

Tun  of  wine  =    250  Imp.  galls. 

SUPPLEMENT. 


327 


FRANCE. 

PORTUGAL. 

Metro  =        3.28  feet. 

100  pounds    = 

101.19  Ibs. 

.  Decimetre  (l-10tli  mutre)        =        8.94  inches. 
Velt     =        2.00  galls. 

22  pounds  (1  arroba)          .  .     = 
4  arrobas  of  32  Ibs.  (1  quintal)  = 

82.00   « 
1.28   " 

Hectolitre      =      26.42     " 

Alquiere        = 

4.75  bush. 

Decalitre       =        2.64     " 

Mojo  of  grain           ..         ..     = 

23.03     " 

Litre    ..         ..         ••         ..     =        2.11  pints. 

Last  of  salt    = 

70.00     « 

Kilolitre        =      35.32  feet 

Almade  of  wino      .  .         .  .     = 

437  galls. 

Hectolitre     =        2.34  bush. 
Decalitre       =        9.'US  quarts. 

PRUSSIA. 

Millier           =      22.U5  Ibs. 

103  Ibs.  of  2  Cologne  marks 

Quintal          =     220.54    " 

each  = 

103.11  Ibs. 

Killogramma           ..         ..     =        2.21    " 

Quintal,  of  110  Ibs  = 

113.42   " 

100  pounds    =     107.93    " 

Sheffel  of  grain       .  .         .  .     = 

1.56  bush. 

100  feet          =     lJ6.60feet 

Eiimr  of  wine         .  .         .  .     = 

13.  14  galls. 

Tun  (of  wine)          .  .         .  .     =     240.00  galls. 

Ell  of  cloth    = 

2.19  feet. 

Foot    = 

1.03  foot 

FLORENCE  AND  LEGHORN. 

"ROME 

100  Ibs.  or  1  cantaro          .  .     =      74.86  Ibs. 
Moggio  of  grain      .  .         .  .     =      16.59  bush. 
Barileofwino         ..         ..     =      12.04  galls. 

JfcW  Ifl  •  1. 

Rubbio  of  grain       .  .         .  .     = 
Barile  of  wine          .  .         .  .     = 
100  Koman  Ibs.        .  .         .  .     = 

8.36  bush. 
15.31  galls. 
74.77  Iba. 

GENOA. 

RUSSIA. 

100  Ibs.  or  peso  grosso      .  .     =      76.87  Ibs. 
100    "    or  peso  sottilo      .  .     =       63.89    " 
Mina  of  grain           ..         ..     =        3.43  bush. 
Mezzarola  of  wine  .  .         .  .     =      39.22  galls. 

100  Ibs.  of  32  loths  each    .  .     = 
Chertwert  of  grain  .  .         .  .     = 
Vedro  of  wine         .  .         .  .     = 
Petersburg  foot       .  .         .  .     = 

90.26  Ibs. 
5.95  bush. 
3.25  galls. 
1.18  foot 

HAMBURG. 

Moscow  foot.  .                    .  .     = 

1.10    " 

Last  of  grain  =      8D.  64  bush. 

Pood   = 

36.  00  Ibs. 

Ahmofwine           ..         ..     =      33.25  galls. 

STCT7Y 

Hamburg  foot          ..         ..     =        0.96  foot. 

Vll                                                             1  oo     u 

DJLvJ-ij  i  « 

Cantaro  grosso        .  .         .       = 

192.50  Ibs. 

Ji-il         .  .            .  .            .  .            .  .       —           l._li 

*.        sottilo                          = 

175  Ibs. 

Jihipfund,  equal  to  2^  cent- 
ners, or  230  Ibs.  Hamburg    =     299  Ibs. 
{8  lispunds,  or 
112  Ibs.  Ham- 
burg. 

lf)0  pounds    = 
Salma  grossa  of  grain        .       = 
"      generale        .  .         .       = 
"      of  wine         .  .         .  .     = 

70    " 
9.77  bush. 
7.85     " 
23.06  galls. 

1  lispund       =      14  Ibs.  Hamburg. 
1  stone  of  flax          ..         ..     =      23    "          " 

SPAIN. 
Quintal,  or  4  arrobas         .  .     = 

131.44  Ibs. 

1  stone  of  wool        ..         ..     =      10    "          " 

Arroba           = 

25.36    " 

1  stone  of  feathers  .  .         .  .     =      13"          " 

"     of  wine         ..         .  .     = 

4.43  galls. 

DO  ibs.  Hamburg   ..         ..     =     106.8  Ibs. 

Paaega  of  grain       .  .                = 

1.GO  bush. 

ITALY. 

ST.  GALL. 

100  rottoli  of  31  3-7  oz.  each    =     19G4  Ibs. 
1  cantaro  grosso       .  .         .  .     =     19G4.    " 

109  heavy  Ibs.          ..         ..     = 

100  light      "            ..         ..     = 

128  Ibs. 
102    " 

MADRAS. 

Candy  =    503  Ibs. 
"     =      20  maunds. 
Maund           =        8  bis. 

SURAT. 

20  Surat  maunds,  or  10  Ben- 
gal factory  maunds.       .  .     = 
1  candy         = 

1  candy. 
746  Ibs.  10  oz. 

Bis       =        8  seers. 

SWSDZIT. 

MALACCA. 
Pecul  =135  Ibs. 

r.Q  Ibs.  or  5  lispunds        .  .     = 
Kan  of  corn  = 
Last               .  .         .  .                = 

73.76  Ibs. 
7.42  bush. 
75  00     " 

^  pecul                                    —  J  10°  catties»  or  !COO 

Cann  of  wine           .  .               = 

69.09  galls. 

\     talcs. 

Ell  of  cloth    = 

1.95  foot 

MALTA. 

2  )  commercial  Ibs  = 

1  lispund. 

100  Ibs.  1  cantaro     ..         ..     =     174.50  Ibs. 
Salma  of  grain         ..         ..     =        8.22  bush. 

20  lispunds    = 

1  skeppund. 

Cantaro         =103  rottoli. 

SMYRNA. 

Kottoli           =      33  oz. 

100  Ibs.  (1  quintal)  .  .         .  .     = 

129.43  Ibs. 

1  cantaro  (mercantile  usage)  =     175  Ibs. 

Oke         ..               ..         ..     = 
Qtiillot  of  grain       ..         ..     = 

2.83    " 
1  .46  bush. 

_    ,                      NAPLES. 
Cantaro  grosso        ..         ..     =     196.50  Ibs. 
picolo        .  .         .  .     =     106.00    " 

Quillot  of  wine       .  .         .  .     = 
TRIESTE. 

13.50  galls. 

Carro  of  grain          ..         ..     -      52.24  bush, 
wine          ..         ..     =    264.00  galls. 

100  pounds    = 
Stajo  of  grain           ..         ..     = 
Orna  or  eimer  of  wine      .  .     = 

123.60  Ibs. 
2.34  bush. 
14.94  galls. 

NETHERLANDS. 

Ell  for  woolens        .  .         .  .     = 
"  for  silk     = 

2.22  feet 
2.10     " 

MuddeofZak         ..        ..     =.-    284.00  bush. 
V  at  hectolitre          .  .         .  .     =      26.42  galls. 

VENICE. 
100  Ibs.  peso  grosso.  .           .     = 

105.1  8  Ibs. 

f>an1li.tr®       =        2.11  pints. 
Pond  killogram™  .  .         ..     =        2.21  Ibs. 
100  pounds    -     108.93    " 

100    "      "     sottile..         ..     = 
Mo<r<rio  of  grain       ..         ..     = 
Anifora  of  wine       .  .        .  .     = 

66.04    " 
9.08  bush. 
137.00  galls. 

328 


SUPPLEMENT. 


TABLE 


GIVING  TUB 


CUMENCY,  EATE  OF  INTEREST, 

PENALTY    FOR    USURY, 

AND  LAWS  IS  REGARD  TO  COLLECTION  OF  DEBTS,  &c., 

IX  THE  SEVERAL  UNITED  STATES. 

THE  following  items  of  information,  it  is  believed,  will  be  found  convenient  for  business  men,  and 
useful  in  the  "Counting-house  and  Family."  They  have  been  collected  with  much  care,  and  original 
sources  resorted  to  in  the  respective  localities,  for  the  most  part.  Yet,  as  the  legislation  in  regard  to 
some  of  these  matters  is  changing,  and  what  is  true  this  year,  in  a  given  State,  may  not  be  entirely  so  the 
next,  some  caution  will  be  required  in  relying  too  implicitly  upon  present  statements,  hereafter.  They 
will  serve,  however,  as  a  general  guide,  and  are  as  valuable  as  any  thing  of  the  sort,  from  the  nature  of 
the  case,  can  well  be. 

Although  the  Federal  Currency  is  that  established  by  law  for  tho  whole  country,  and  that  in  common 
use  in  all  the  btates,  yet,  as  previous  to  its  adoption  tho  different  States  had  different  usages  in  these 
respects,  that  ancient  usage,  to  some  extent,  continues.  Thus,  in  Massachusetts,  six  shillings  make  a 
dollar,  in  ^e\v  York,  eight  shillings,  &c. 


MAINE. 

Currency. — The  dollar  is  6s. ;  Is.  is  lG"c. ;  6J.  is 
&£c. ;  9d.,  12|c.,  &c. 

Interest. — Six  per  cent. 

Penalty  for  Usury, — Usurious  excess  void.  For 
debts  contracted  out  of  the  State,  the  rates  of  in- 
terest in  that  State  aro  supported  by  our  laws ;  i.  e. 
a  debt  contracted  in  California,  interest  12  per 
cent.,  both  parties  remove  here  and  note  still  due, 
interest  continues  the  same  as  where  it  began. 

Collection  of  Debts. — He.tl  estate,  and  goods  and 
chattels,  may  be  attached  and  held  as  security  to 
satisfy  a  judgment,  which  must  be  rendered  by  the 
appropriate  court.  Property  possessed  by  a  woman 
before  marriage,  remains  hers  after  marriage,  and 
not  liable  for  husband's  debts.  Arrest  for  debt 
allowed  if  party  about  to  leave  the  State,  but  if  he 
disclose  he  is  discharged,  if  he  has  not  wherewithal 
to  pay  the  debt.  Certain  specified  property,  for 
current  support,  exempt  from  attachment.  There 
is  a  homestead  exemption  and  mechanics'  lien  law. 

NEW  HAMPSHIRE. 

Currency. — Same  as  Maine. 

Interest. — Six  per  cent. 

Penalty  for  Usury.— Forfeiture  of  threo  times 
the  usury. 

Collection  of  Dfl>U.— There  is  a  mechanics1  lien 
and  homestead  exemption  law.  Certain  specified 
property  is  also  exempted  from  attachment  Other 
real  and  personal  estate  may  be  attached.  Mort- 
gages of  personal  property  must  be  recorded  in 
town  clerk's  office. 

VERMONT. 

Currency. — Same  as  Maine. 

Interest.— Six  per  cent.  Unusual  interest  legal 
when  contracted  for. 

Penalty  for  Usury. — Excess  not  collectable,  and 
when  paid  may  be  recovered  back  and  costs. 

Collection  of  Debts.— Heal  and  personal  property 
may  be  attached  on  mesne  process,  and  persons 
jesiding  in  tho  State  owing  debtor  exceeding  $10 


may  be  trusteed.  Xo  imprisonment  on  contract, 
except  on  affidavit  that  debtor  is  about  to  remove 
from  the  State  and  has  money  or  property  secreted 
Mechanics  have  a  lien  for  a  limited  time.  Home- 
stead exemption,  $500.  Household  furniture,  cloth- 
ing, and  tools,  exempt  from  attachment. 

MASSACHUSETTS. 

Currency. — Some  as  Maine. 

Interest. — Six  per  cent. 

Penalty  for  Usury.— Three  times  the  unlawful 
interest  taken.  A  Lank  taking  unlawful  interest 
forfeits  the  debt. 

Collection  of  Debts.— A  mechanics' lien  and  home- 
stead exemption  law.  Other  specified  property  for 
fumily  use  and  carrying  on  trade,  exempt  from  at- 
tachment. Mortgages  of  personal  property  to  bo 
recorded  by  town  clerk.  Keal  and  personal  prop- 
erty not  exempted,  attachable.  Imprisonment  for 
debt  not  allowed  except  for  fraud.  Two  thirds  in 
value  of  the  creditors  may  put  a  debtor  into  insolv- 
ency, when  all  his  property  shall  be  applied  ibr 
equal  benefit  of  all  creditors  in  proportion  to  claims 
proved  ;  or  any  creditor  of  $100  and  upwards  may, 
for  specified  causes,  compel  debtor  to  insolvency. 
Debtor  complying  with  certain  conditions  and  giv- 
ing up  all  property,  not  further  liable  for  any  debts 
thereafter  in  the  State.  Married  women  have  in- 
dependent rights  of  property. 

RHODE  ISLAND 

Currency. — Same  ns  Maine. 

Legal  Interest. — Six  per  cent. 

Penalty  for  Usury. — Forfeiture  of  excess. 

Collection  of  Debts. — Mechanics' lien  law.  Speci- 
fied property  exempt  from  attachment ;  other  prop- 
erty may  be  attached.  Mortgages  of  personal  prop- 
erty must  Jfce  recorded  in  town  clerk's  office.  Im- 
prisonment for  debt  allowed,  but  the  jail  limit.3 
extend  to  the  county.  Here,  as  in  most  of  tho 
States,  unwitnessed  notes  and  ordinary  book  ac- 
counts can  not  be  sued  for  after  six  years,  unless  9- 
formal  judgment  of  court  shall  have  been  had. 


SUPJ'LEM  ENT, 


32 


CONNECTICUT. 

Currency. — Same  as  Maine. 

Interest.— Six  per  cent. 

Usury. — Forfeiture  of  all  interest. 

Collection  of  Debts. — A  mechanics1  lien  law. 
Other  specified  property  exempted  from  attach- 
ment. Mortgager  of  personal  property  may  retain 
possession  of  it.  Goods,  chattels,  and  real  estate  of 
debtor  may  be  attached,  subject  to  be  defeated  by 
insolvency  within  sixty  days.  Person  of  debtor 
not  liable  to  arrest  Wife's  property  at  time  of 
marriage,  or  subsequently  acquired  by  devise  or 
inheritance,  not  liable  for  husband's  debts. 


NEW  YORK. 

Currency.— T)o\\*r,  8  shillings;  Is.,  12*0.;  6d.,  GJc. 

Legal  Interest.— Seven  per  cent. 

Penalty  for  Usury. — Voids  the  contract,  but 
corporations  can  not  set  up  usury  as  defense.  Per- 
sons who  take  usury  deemed  guilty  of  a  misde- 
meanor and  liable  to  a  flue  not  exceeding  $100,  or 
imprisonment  not  exceeding  six  months,  or  both. 

Collection  of  Debts.— Certain  specified  property 
exempt  from  attachment;  also  a  homestead  ex- 
emption to  value  of  $1000,  and  continued  for  benefit 
of  widow  and  children  until  youngest  child  21. 
But  the  deed  conveying  the  property  must  show  it 
intended  to  be  held  as  such  homestead,  or  a  precise 
notice  given  and  recorded  to  that  effect.  Mechan- 
ics, laborers,  &c.,  in  all  cities  and  certain  counties, 
have  a  lien  on  buildinss.  <fcc.,  for  pay  for  labor,  ma- 
terials, Ac.,  on  such  buildings.  Chattel  mortgages 
void  unless  filed  with  town  or  county  clerks,  or 
goods  delivered.  Personal  arrest  allowed  in  case 
of  fraud,  concealment,  &c.  Property  owned  by 
female  at  marriage  not  liable  for  husband's  debts. 
Married  woman  may  hold  separate  property,  taken 
by  inheritance,  or  by  gift  or  bequest  from  any  per- 
son other  than  the  husband,  and  the  same  shall  not 
be  liable  for  the  debts  of  the  husband,  nor  subject 
to  his  disposal. 

NEW  J3E3ET. 

Currency. — 7s.  6d.  to  the  dollar. 

Interest. — Six  per  cent. 

Paltry. — Forfeiture  of  whole  amount. 

Collection  of  Debts.— Homestead  exemption  to 
amount  of  $1000.  Other  specified  property  ex- 
empt from  attachment.  A  mechanics'  lien  law. 
Ordinary  debts  outlawed  in  six  years.  Females 
exempt"  from  arrest  for  debt.  Widows1  right  of 
dower,  one  third  husband's  real  estate. 


PENNSYLVANIA. 

Currency.— Is.  6d.  to  the  dollar ;  121  cts.  called  a 
levy,  an  abbreviation  of  eleven  pence ;  6£  cts. 
an  abbreviation  of  five  pence  orjippenny  bit. 

Legal  Interest. — Six  per  cent. 

Penalty  for  Usury. — Forfeiture  of  usurious  in- 
terest in  action  on  the  contract,  and  of  the  money 
lent  in  a  penal  action. 

Collection  of  Debt*.— Property  to  amount  of  $300, 
and  clothing,  school  books,  &c.,  exempt  from  at- 
tachment. Mechanics  have  lien  on  buildings  for 
labor  an  I  materials  in  their  construction  in  most  of 
the  coanties.  Arrest  of  person  of  debto^  not  al- 
lowed except  for  fraud  or  concealment.  Six  years 
voids  debts  by  simple  contract.  Women's  individ- 
ual right  in  property  continues  after  marriage,  as 
before. 


DELAWARE. 

Currency.— -7s.  6d.  to  the  dollar. 

Rate  of  Interest. — Six  per  cent. 

Penalty  for  Usury. — i  orfeiture  of  debt. 

Collection  of  Debts.— Specified  property,  not  ex- 
ceeding $100,  exempted  from  attachment.  Person 
of  debtor  may  not  be  arrested,  except  for  fraud, 
concealment,  <fec.  Limitation  of  debts,  not  of  rec- 
ord, three  years;  for  recovery  of  land,  twenty 
years;  note  of  hand,  six  years. 

MARYLAND. 

Currency. — 7s.  6d.  to  the  dollar,  but  shillings  and 
pence  are  abolished  in  law  and  obsolete  in  popular 
use. 

Interest. — Six  per  cent. 

Usury. — Forfeiture  of  usury. 

Collection  of  Debts. — Mechanics  and  men  supply- 
ing material  have  a  lien  in  Baltimore  city  and  most 
of  the  counties  for  work  done  and  materials  furnished 
on  and  for  the  construction  of  buildings.  Property 
belonging  to  a  woman  not  liable  for  payment  of 
husband's  debts.  Wearing  apparel  and  bedding  of 
debtor  and  family  exempt  from  execution.  Mort- 
gages of  personal  property  must  be  in  writing, 
acknowledged,  and  recorded  within  twenty  days  of 
their  date.  Actions  for  debt,  not  on  a  seale'd  instru- 
ment, must  be  brought  within  three  years;  on 
sealed  instruments  within  twelve  years.  Xo  im- 
prisonment for  debt. 

VIRGINIA. 

Currency. — 6s.  to  the  dollar. 

Interest. — Six  per  cent. 

Usury. — Renders  contract  void,  and  in  criminal 
action  forfeits  double  the  value  of  money  lent. 

Collection  of  Debts.  —  Mechanics  have  lien  on 
land  upon  which  they  erect  buildings,  provided 
they  build  by  contract  in  writing  and  recorded. 
Growing  crops,  not  severed,  not  liable  to  distress 
or  levy,  except  Indian  corn,  which  may  be  taken 
after  15th  October.  Specified  articles  also  exempt- 
ed. Slaves  not  to  be  distrained  or  levied  upo*a 
without  debtor's  consent,  where  other  effects  suffi- 
cient are  shown  to  o.licer,  and  in  his  power  to  take. 
Mechanics1  tools  exempt  to  value  of  twenty-five 
dollars.  Actions  on  unsealed  instruments  barred 
generally  in  five  years;  on  sealed  instruments  in 
ten  and  twenty  years.  Imprisonment  for  debt 
abolished.  In  certain  cases,  debtor,  when  sued, 
maybe  held  to  bail;  ani  in  default  of  giving  bail 
may  be  imprisoned.  Married  women  may  hold 
property  separate  from  their  husbands.  Widow's 
dower,  one  third  of  real  estate  for  life,  and  of  per- 
sonal estate  absolutely  after  payment  of  debts,  ex- 
cept only  life  estate  in  slaves. 

Judgments  sive  lien  on  real  estate  from  first  day 
of  the  term  of  the  court  at  which  they  are  rendered. 
Executions  bind  all  the  personalty  which  tb.3 
debtor  possesses,  or  to  which  he  is  entitled,  from 
the  moment  they  are  in  the  hands  of  an  officer 
who  can  by  law  levy  them  ;  and  jtidsment  debtor 
may  be  compelled,  by  interrogatories  filed  before  a 
commissioner  in  chancery,  to  disclose  upon  oath 
all  his  effects,  real,  personal,  and  mixed,  in  his  pos- 
session or  under  his  control.  If  he  answer  said 
interrogatories  fraudulently,  or  evasively,  the  com- 
missioner may  attach  and  commit  him.  Any  ona 
indebted  to  a  judgment  debtor  may  be  garnished 
by  the  judsment  Creditor,  and  made  to  pay  such 
creditor.  Elegits  now  extend  to  all  debtor's  real 
estate.  Judgment  creditors  may  sue,  at  law  or  in 
equity,  at  their  own  costs,  in  name  of  sheriff  or 
other  officer,  to  recover  any  property  of  their  debt- 
ors, on  which  they  obtain  a  lien. 


330 


SUPPLEMENT. 


NORTH  CAROLINA, 

Currency. ~-  10s.  to  the  dollar. 

Interest—Six  per  cent. 

Usury.— Voids  the  contract;  lender  forfeits 
double  the  amount  of  money  lent. 

Collection  of  Debts. — Specified  property  exempt 
from  attachment.  Actions  on  simple  contract 
must  be  brought  within  three  years;  for  land, 
eeven  years ;  by  infants,  feme  coverts,  or  non  com- 
pos mentis,  within  three  years  after  disability  re- 
moved; persons  beyond  seas,  within  eight  years 
after  title  accrues.  Possession  for  twenty-one 
years,  under  color  of  title,  a  bar  to  the  State. 
Three  years'  possession  of  personal  property  gives 
title.  Wife's  real  estate  at  time  of  marriage  can 
not  be  sold  or  leased  by  husband  without  consent 
of  wife.  Deeds,  mortgages,  marriage  settlements, 
&c.,  must  be  recorded,  or  are  void  as  to  creditors. 

SOUTH  CAROLINA. 

Currency. — 4s.  8d.  to  the  dollar. 

Interest. — Seven  per  cent. 

Usury. — Forfeiture  of  interest  with  costs. 

Collection  of  Debts.— Attachment  holds  against 
the  property  of  a  non-resident  or  absconding  debt- 
or, and  the  person  of  a  debtor  about  to  abscond. 
Actions  for  debt  must  be  brought  within  four  years ; 
to  recover  possession  of  land,  within  ten  years. 
Deeds  of  marriage  settlement  must  be  recorded. 
Mechanics  have  lien  on  building.  Chattel  mortga- 
ges void  as  against  subsequent  purchasers,  unless 
recorded.  Specified  property,  and  a  house  and  fifty 
acres  of  land,  exempted  from  attachment,  to  $500. 

GEORGIA. 

Currency. — 4s.  8d.  to  the  dollar. 

Interest. — Seven  per  cent. 

Usury. — Usurious  interest  only  void,  principal 
and  legal  interest  recoverable. 

Collection  of  Debts.— AM  actions  under  the  com- 
mon law  of  England  in  force  in  this  State.  Me- 
chanics have  a  lien  on  buildings  they  have  built  or 
repaired.  Liens  on  river  steam-boats  for  wages, 
provisions,  supplies,  and  repairs;  the  same  lien 
extends  over  mills  for  lumber,  wages,  provisions 
furnished,  and  repairs.  There  is  a  homestead  ex- 
emption from  levy  and  sale,  but  the  property  must 
not  exceed  in  value  $230.  All  conveyances  of  land 
must  be  recorded  within  six  months ;  all  mortga- 
ges, both  of  real  and  personal  estate,  must  be  re- 
corded within  ninety  days.  Actions  on  open  ae- 
count3»mu3t  be  brought  within  four  years;  on 
promissory  notes,  unsealed,  six  years;  for  recovery 
of  land,  seven  years ;  on  bonds  ami  other  sealed 
instruments,  twenty  years.  All  property  of  what- 
ever kind  subject  to  attachment.  Honest  debtors' 
act  in  force;  its  operation  is  to  release  the  debtor's 
person  from  arrest,  but  not  his  present  or  any 
future  property  from  levy.  Wives  and  widows  are 
not  exempt  from  the  operation  of  the  attachment 
law;  but  the  persons  of  all  women  in  Georgia  are 
exampt  from  arrest  under  any  civil  process. 

ALABAMA, 

Currency.— Federal  money  only. 

Interest.— Eisrht  per  cent. 

Usury.— Forfeits  all  interest. 

Collection  of  Debt*.— Specified  articles  and  home- 
stead to  value  of  $500  exempt  from  execution  and 
sale.  Mechanics'  lien  law.  Actions  on  liquidated 
demands  must  be  brought  within  six  years;  on 
open  account,  in  three  years.  Mortgages  of  real 
and  personal  property  must  be  recorded.  Sale  of 
goods  over  $200  must  be  evidenced  by  transfer  of 


some  portion  of  the  goods,  or  payment  of  somo 
portion  of  purchase  money,  or  written  contract 
Attachment  lies  for  debts,  whether  now  due  or 
not,  in  case  of  fraud  in  the  debtor  and  non-resi- 
dence. Arrest  of  person  allowed,  if  fraud  or  con- 
cealment. Husband  acquires  no  right  to  wife's 
property  by  marriage,  so  as  to  make  it  liable  for 
his  debts,  but  is  entitled  to  its  management  and 
control  during  coverture ;  and  husband  and  wife 
are  jointly  liable  for  family  supplies. 


MISSISSIPPI. 

Currency. — 8  bits  (12£  cents)  to  the  dollar. 

Interest.— Six  per  cent.,  or  by  contract  in  writ- 
ingfor  money  lent,  any  rate  of  interest  not  exceed- 
ing ten  per  cent. 

Usury.— Forfeiture  of  interest. 

Collection  of  Debts.— No  imprisonment  of  debtor. 
Mortgages  and  deeds  of  trust  must  be  acknowl- 
edged and  recorded.  Specified  property  and  a 
homestead  exempted  from  execution  and  attach- 
ment. A  mechanics'  lien  law.  Actions  on  notes 
and  bills,  limited  to  six  years ;  open  accounts  for 
goods  sold,  three  years;  bonds  and  sealed  instru- 
ments, seven  years ;  possession  of  land,  ten  years. 
Property  of  wife  only  sold  by  joint  deed  of  herself 
and  husband. 

LOUISIANA. 

Currency. — Federal  money,  only  in  New  Orleans 
a  picayune  is  6  lr  cents. 

Interest. — Five  per  cent;  by  agreement  of  parties, 
ten  per  cent.  Bank  interest,  five  to  eight  per  cent 

Usury.— Forfeiture  of  interest. 

Collection  of  Debts.  —  A  mechanics'  lien  law. 
Specified  property  exempt  from  attachment.  "Wo- 
men not  subject  to  arrest  for  debt  Property  owned 
by  either  party  before  marriage  remaining  such 
afterward.  No  imprisonment  for  debt 

FLORIDA. 

Currency. — Federal  money  only. 

Interest. — Six  per  cent,  or  by  agreement,  eight. 

Usury. — Forfeits  interest. 

Collection  of  Debts.  —  Imprisonment  for  debt 
abolished.  Specified  property  and  forty  acres  of 
land  exempt  from  attachment,  not  exceeding  $200  ; 
also  dwelling  house  to  same  amount  by  city  or 
town  resident.  A  mechanics'  lien  law.  Mortgages 
of  personal  property  must  be  recorded.  Widow's 
dower,  life  interest  in  one  third  of  real  estate. 
Wife's  property  at  marriage  continues  hers,  and  not 
liable  for  husband's  debts. 


TEXAS. 

Currency. — Federal  money. 

Interest. — Eight  per  cent,  or  higher  to  twelve  per 
cent.,  by  agreement. 

Usury. — Forfeits  interest. 

Collection  of  Debts. — Mortgages  of  personal  prop- 
erty must  be  recorded,  and  may  be  set  aside  for 
valuable  consideration,  or  possession  given  to  mort- 
gagee. Actions  for  debt  on  account  must  be  brought 
within  two  years;  on  contract,  four  years;  real 
estate,  varying  with  circumstances.  A  homestead 
exemption;  specified  personal  property  r.lso  ex- 
empted from  attachment.  A  mechanics'  lien  law. 
No  imprisonment  for  debt.  Property  attachable 
of  debtor  non  est.  Widow's  dower,  life  interest  in 
one  third  real  estate.  Property  of  feme  sole  fit  mar- 
riage, if  registered,  remains  hers  independently. 


SUPPLEMENT. 


331 


TENNESSEE. 

Currency. — 6s.  to  the  dollar. 

Interest.— Six  per  cent, 

Usury—  Fine  at  least  $10. 

Collection  of  Debts.— Specified  property  exempt 
from  attachment.  A  mechanics'  lien  law.  Mort- 
gages of  personal  property  must  be  recorded.  ><'o 
imprisonment  for  debt.  Property  of  concealing  or 
absconding  debtor  attachable.  Actions  for  dubU 
of  account  must  be  brought  within  three  years. 
Widow's  dower,  one  third  of  husband's  estate  at 
death.  Married  women,  the  twain  are  not  one  as 
to  wife's  property,  in  which  she  has  an  independent 
ri^ut  A  hoineoteal  exemption. 

KENTUCKY. 

Currency. — 6s.  to  tho  dollar. 

Interest. — Six  per  cent. 

Usury. — Forfeiture  of  usury  and  costs. 

Collection  of  Debts.— Mortgages  of  personal  and 
real  property  must  be  recorded.  A  mechanics' 
lien  law  in  certain  towns.  Specified  property  ex- 
empt from  attachment.  Debtor  is  held  to  bail  on 
specified  conditions.  Property  attachable  in  case 
of  concealment,  proposed  removal,  absence,  &c. 
Feme  covert  has  independent  rights  in  property, 
but  husband  not  liable  for  wife's  debts  before  mar- 
riage. Actions  limited,  on  account,  to  one  year. 

OHIO. 

Currency.— -Ss.  to  the  dollar. 

Interest.— Sis.  per  cent  As  high  as  ten  per  cent, 
if  stipulated  in  written  instrument.  Banks  allowed 
only  six  per  cent. 

Usury.— Forfeiture  of  usury. 

Collection  of  Debts.—  Mecuanics'  lien.  Specified 
property  exempt  from  execution.  A  homestead 
exemption.  Mortgages  of  personal  property  valid 
for  one  year  if  recorded.  Lands  not  to  be  sold  for 
Jess  than  two  thirds  of  the  appraised  value.  Attach- 
ments allowed  in  specified  cases.  First  attachment 
of  prior  validity.  Limitation  laws:  real  estate, 
twenty-one  year's;  written  contracts,  fifteen  years; 
not  written,  six  years.  Widow's  dower,  one  third 
of  real  estate. 

INDIANA. 

Currency. — 63.  to  the  dollar. 

Interest.— Six  per  cent 

Usury.— Forfeiture  of  nsnrions  interest. 

Collection  of  Debts. — Mechanics'  lien  law.  Home- 
stead exemption  law.  Specified  property  exempt 
from  attachment.  Mortgages  of  personal  property 
must  be  acknowledged  and  recorded  unless  prop- 
erty transferred.  Ordinary  debts  outlawed  in  six 
years  ;  contracts  in  writing  and  real  estate.  Real 
and  personal  property  not  specially  exempted  may 
be  taken  on  execution.  Wife's  real  estate  at  or 
after  coverture,  not  liable  for  husband's  debts. 

ILLINOIS. 

Currency.— Federal  money. 
Interest. — Six  per  cent. ;  by  agreement,  as  high 
as  ten  per  cent 

Usury. — Forfeits  entire  interest. 

Collection  of  Debt*.— Widow's  dower,  one  third 
of  real  estate.  A  mechanics' lien  law.  Homestead 
exemption  law.  Specified  articles  not  attachable. 
Chattel  mortgages  must  be  acknowledged  and  re- 
corded or  property  delivered.  Body  of  debtor  may 
be  arrested  for  fraud  or  concealment. 


MICHIGAN. 

Currency. — Ss.  to  the  dollar. 

Interest.— Seven  per  cent.,  yet  as  high  as  ten  per 
cent  by  agreement  of  parties. 

Usury. — Voids  the  excess. 

Collection  of  Debts.— There  is  a  mechanics'  lien 
law,  and  a  homestead  exemption  law.  Mortgages 
of  personal  property  must  be  recorded,  and  then 
are  void,  as  against  other  creditors  or  mortgagees, 
after  one  year,  unless  within  thirty  days  preceding 
an  authenticated  certificate  is  attached  to  the  in- 
strument or  record  setting  forth  mortgagee's  inter- 
est Contracts  for  sale  of  goods  invalid  above  $50, 
unless  part  of  goods  delivered,  or  something  given 
to  bind  the  bargain.  Actions  for  ordinary  debts 
must  be  brought  within  six  years.  Person  of 
debtor  may  be  arrested,  if  debtor  about  to  remove 

Eroperty  from  State,  or  fraudulent  concealment  or 
itent  to  defraud.  Feme-  coverfs  right  to  property 
possessed  before  marriage,  or  to  which  she  becomes 
entitled  subsequently,  continues  her  separate 
property,  and  not  liable  for  husband's  debts,  and 
she  may  alienate  it  as  if  unmarried. 

MISSOTJBL 

Currency.— -6s.  to  the  dollar ;  bit,  12J  cts. ;  pica- 
yune, 6'f  cts. 

Interest.— Six  per  cent ;  by  agreement,  as  high 
as  ten. 

Usury. — Forfeits  usury  and  interest 

Collection  of  Debts.— Wife's  dower,  life  estate  in 
one  third  real,  and  specified  personal  property  ab- 
solutely. Wife's  property  at  marriage  not  liable 
for  husband's  old  debts.  No  imprisonment  for 
debt.  Attachment  of  property  in  case  of  fraud, 
concealment,  or  removal  of  property,  or  non-resi- 
dence. Property  not  specially  exempt  may  be 
taken  on  execution.  Mortgages  of  personal  prop- 
erty must  be  recorded.  Suits  on  open  account 
debts  must  be  brought  within  five  years ;  on  store 
accounts,  two  years;  on  notes,  bonds,  bills.  &c.. 
ten  years.  Specified  property  exempt  from  sale  on 
execution.  A  mechanics'  lien  law. 

IOWA. 

Currency. — Federal  money. 
Interest.— Sis.  per  cent.,  and  up  to  ten  by  agree- 
ment. 

Usury.— Usurious  interest  recoverable. 

Collection  of  Debts. — A  mechanics'  lien  law.  A 
household  exemption  law.  Specified  property  ex- 
empt from  attachment  Mortgages  of  personal 
property  must  be  recorded.  Ordinary  indebted- 
ness outlawed  in  five  years ;  written  contracts,  as 
notes,  <fec.,  ten  years.  Person  of  debtor  exempt 
from  arrest  Married  woman  has  rights  in  prop- 
erty independent  of  husband. 

WISCONSIN. 

Currency. — Federal  money. 

Interest.— Seven  per  cent. ;  as  high  as  twelve  bj 
agreement 

Utsury. — Forfeiture  of  entire  debt 

Collection  of  Debts.— A.  mechanics'  lien  law.  A 
homestead  exemption.  Mortgages  of  personal  prop- 
erty must  be  filed  or  recorded.  Actions  for  recov- 
ery of  ordinary  debts  must  be  commenced  within 
six  years.  No  imprisonment  for  debt,  but  property 
of  debtor  attachable  under  certain  circumstances. 
Real  and  personal  estate  of  feme  sole  not  liable  for 
husband's  debts. 


332 


SUPPLEMENT. 


MINNESOTA. 

Currency. — Federal  money. 

Interest.— Seven  per  cent.,  or  any  higher  rate  if 
agreed  in  writing. 

Usury. — No  usury  law. 

Collection  of  Debts. — A  mechanics'  lien.  A 
homestead  exemption  law.  Specified  property  ex- 
empt from  attachment.  Mortgages  of  personal 
property,  a  copy  must  be  filed  with  or  recorded 
by  county  register.  Imprisonment  for  debt  abol- 
ished. Contracts  for  sale  of  goods  must  be  in  writ- 
ing for  amounts  over  $50,  unless  part  of  goods 
delivered,  or  part  of  purchase  money  or  considera- 
tion paid.  Keal  and  personal  estate  of  feme  sole 
not  liable  for  husband's  debts  after  marriage. 
"Widow's  dower,  life  interest  in  ono  third  real  es- 
tate. 

CALIFORNIA. 

Currency. — Federal  money,  but  usage  not  wholly 
established. 

Interest. — Ten  per  cent. ;  any  higher  rate  by 
contract  not  exceeding  18. 

Usury. — Forfeiture  of  excess. 

Collection  of  Debts.— Mechanics'  lion  law.  Home- 
stead exemption  law.  Specified  property  exempt 
from  attachment  Mortgages  of  personal  property, 
property  must  bp  transferred.  Contracts  void  if 
over  $200,  unless  in  writing,  or  part  payment  made, 
or  part  goods  delivered.  Property  may  be  at- 
tached, although  debt  not  due.  if  fraud,  conceal- 
ment, or  absconding.  Wife  holds  in  separate  right 
property  owned  by  her  before  marriage. 

DISTRICT  Oj1  COLUHI3IA. 

Currency.— Federr.l  money. 

Interest. — Six  per  cent. 

Usury.— Voids  contracts  at  laxr,  but  a  complain- 
ant in  equity  is  relieved  only  as  to  the  excess. 

Collection  of  Debts. — Debts  of  $50  or  less  are  re- 
coverable speedily  before  a  justice;  above  that,  in 
Circuit  Court.  Where  matter  in  controversy  is 
$1000,  appeal  lies  to  Supreme  Court.  Money  in  the 
treasury  cannot  be  attached,  but  a  party  having  tho 
apparent  right  to  receive  money  from  the  treasury, 
may  be  enjoined  from  receiving  the  same  by  his 
assignee  or  otiiar  person  Laving  tiie  substantial 


equitable  title  to  that  very  fund.    No  bail  in  civil 
cases  ;  no  imprisonment  for  debt. 

NOVA  SCOTIA. 

Currency.— 5s.  or  J  pound  to  the  dollar. 

Interest.— Six.  per  cent. 

J'enaliy  for  Usury.— Forfeiture  of  treble  tho 
amount ;  does  not  extend  to  any  hypothecation  or 
agreement  in  writing  entered  into  for  money  ad- 
vanced upon  the  bottom  of  a  ship  or  vessel,  her 
cargo  or  freight. 

Collection  of  Debts.— In  tho  Supreme  Court, 
major's  and  magistrate's  courts  by  civil  summons; 
capias  where  parties  are  about  to  quit  the  province. 
Limitation  laws ;  written  contracts  under  seal, 
twenty  years  ;  ordinary  contracts,  six  years.  Mort- 
gages of  personality,  same  as  under  the  English  law. 
Widow's  dower,  ono  third  of  real  estate  and  one 
third  of  personality. 

CANADA. 

Currency. — 4s.  sterling  equals  4s.  IP^d.  currency 
at  the  banks.  Elsewhere,  4s.  sterling  equals  5s. 
currency.  Is.  currency,  20  cents.  5s.  currency  to 
the  dollar.  $4  to  the  pound. 

Interest.— Six  per  cent,  at  banks.  Elsewhere,  any 
rate  of  interest  agreed  upon ;  but  no  more  than  six 
per  cent,  can  bo  recovered  at  la^c,  even  where  a 
higher  rate  may  have  been  stipulated. 

Usury — Penalties  for  usury  abolished,  except  as 
regards  banks. 

Collection  of  Debts. — No  homestead  exemption. 
Specified  articles  not  seizablc.  "When  married  here, 
without  a  marriage  contract,  the  wife's  dower  is 
the  half  of  the  real  estate  the  husband  has  at  the 
time  of  tho  marriage,  or  which  he  may  acquire  by 
inheritance  during  the  marriage.  Mortgages  on 
real  estate  obtain  precedence  of  payment  according 
to  the  date  of  their  registration.  No  mortgages 
obtainable  on  personal  property.  No  seizure  of 
estate  for  debt  before  judgment,  except  where  a 
creditor  swears  his  debtor  is  fraudulently  conceal- 
ing or  disposing  of  it.  No  imprisonment  for  debt, 
except  when  a  debtor  is  leaving  the  province  of 
Canada  with  a  fraudulent  intent.  Limitation  laws: 
possession  for  thirty  years  creates  a  title ;  when 
proprietor  is  in  a  foreign  country,  twenty  years. 


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